Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- ETD (30)
- Publications (17)
- Mathematics (10)
- Maximum likelihood estimation (9)
- Trees (8)
-
- Applications (5)
- Interior-point method (5)
- Linear complementarity problem (5)
- Mathematics education (5)
- Wiener index (5)
- Cartesian product (4)
- Coadjoint orbit (4)
- Edge-coloring (4)
- Generalized Distribution (4)
- Generating functions (4)
- Graph theory (4)
- Inverse Weibull Distribution (4)
- Moments (4)
- Q-series (4)
- Refereed Publications (4)
- Research Papers (4)
- STEM (4)
- Algebraic geometry (3)
- Bailey pairs (3)
- Bijection (3)
- Chaos (3)
- Chemical Graph Theory (3)
- Chromatic number (3)
- Circle method (3)
- Combinatorics (3)
- Publication Year
- Publication
-
- Department of Mathematical Sciences Faculty Publications (194)
- Theory and Applications of Graphs (121)
- Electronic Theses and Dissertations (62)
- Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators (42)
- Honors College Theses (11)
-
- Enkeleida K. Lakuriqi (8)
- Alina Iacob (6)
- Department of Mathematical Sciences Faculty Presentations (6)
- Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (5)
- Legacy ETDs (4)
- Zhan Chen (4)
- Colton Magnant (3)
- François Ziegler (3)
- Saeed Nasseh (3)
- Yi Lin (3)
- College of Science and Mathematics Faculty Presentations (2)
- Georgia Educational Researcher (2)
- National Youth Advocacy and Resilience Conference (2)
- Scott N. Kersey (2)
- Xiezhang Li (2)
- Yi Hu (2)
- Andrew V. Sills (1)
- Broderick O. Oluyede (1)
- Department of Psychology Faculty Publications (1)
- Finding Aids (1)
- GS4 Georgia Southern Student Scholars Symposium (1)
- Georgia Educational Research Association Conference (1)
- Sze-Man Ngai (1)
- Teaching and Learning Faculty Presentations (1)
- Yingkang Hu (1)
Articles 1 - 30 of 496
Full-Text Articles in Entire DC Network
Approval Gap Of Weighted K-Majority Tournaments, Jeremy Coste, Breeann Flesch, Joshua D. Laison, Erin Mcnicholas, Dane Miyata
Approval Gap Of Weighted K-Majority Tournaments, Jeremy Coste, Breeann Flesch, Joshua D. Laison, Erin Mcnicholas, Dane Miyata
Theory and Applications of Graphs
A $k$-majority tournament $T$ on a finite set of vertices $V$ is defined by a set of $2k-1$ linear orders on $V$, with an edge $u \to v$ in $T$ if $u>v$ in a majority of the linear orders. We think of the linear orders as voter preferences and the vertices of $T$ as candidates, with an edge $u \to v$ in $T$ if a majority of voters prefer candidate $u$ to candidate $v$. In this paper we introduce weighted $k$-majority tournaments, with each edge $u \to v$ weighted by the number of voters preferring $u$.
We define the …
Strongly I-Bicritical Graphs, Michelle Edwards, Gary Macgillivray, Shahla Nasserasr
Strongly I-Bicritical Graphs, Michelle Edwards, Gary Macgillivray, Shahla Nasserasr
Theory and Applications of Graphs
A graph $G$ is \emph{strongly $i$-bicritical} if it has independent domination number $i(G) \geq 3$, and $i(G - \{x, y\}) = i(G) - 2$ whenever $x$ and $y$ are two non-adjacent vertices of $G$. We describe five constructions of strongly $i$-bicritical graphs. For four of them, necessary and sufficient conditions for the graph produced by the construction to be strongly $i$-bicritical are given. The strongly $i$-bicritical graphs with independent domination number $i(G) = 3$ are characterized, and it is shown that the strongly $i$-bicritical graphs with independent domination number $i(G) \geq 5$ may be hard to characterize. It is shown …
Recent Studies On The Super Edge-Magic Deficiency Of Graphs, Rikio Ichishima, Susana C. Lopez, Francesc Muntaner, Yukio Takahashi
Recent Studies On The Super Edge-Magic Deficiency Of Graphs, Rikio Ichishima, Susana C. Lopez, Francesc Muntaner, Yukio Takahashi
Theory and Applications of Graphs
A graph $G$ is called edge-magic if there exists a bijective function $f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left(G\right) \right\vert \right\}$ such that $f\left(u\right) + f\left(v\right) + f\left(uv\right)$ is a constant for each $uv\in E\left( G\right) $. Also, $G$ is called super edge-magic if $f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}$. Furthermore, the super edge-magic deficiency $ \mu_{s}\left(G\right)$ of a graph $G$ is defined to be either the smallest nonnegative integer $n$ with the property that $G \cup nK_{1}$ is super edge-magic or $+ \infty$ if there exists no such …
A Survey Of Maximal K-Degenerate Graphs And K-Trees, Allan Bickle
A Survey Of Maximal K-Degenerate Graphs And K-Trees, Allan Bickle
Theory and Applications of Graphs
This article surveys results on maximal $k$-degenerate graphs, $k$-trees,
and related classes including simple $k$-trees, $k$-paths, maximal
outerplanar graphs, and Apollonian networks. These graphs are important
in many problems in graph theory and computer science. Types of results
surveyed include structural characterizations, enumeration, degree
sets and sequences, chromatic polynomials, algorithms, and related
extremal problems.
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Honors College Theses
The properties of n-color compositions have been studied parallel to those of regular compositions. The conjugate of a composition as defined by MacMahon, however, does not translate well to n-color compositions, and there is currently no established analogous concept. We propose a conjugation rule for cyclic n-color compositions. We also count the number of self-conjugates under these rules and establish a couple of connections between these and regular compositions.
Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly
Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly
Electronic Theses and Dissertations
In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …
Classification In Supervised Statistical Learning With The New Weighted Newton-Raphson Method, Toma Debnath
Classification In Supervised Statistical Learning With The New Weighted Newton-Raphson Method, Toma Debnath
Electronic Theses and Dissertations
In this thesis, the Weighted Newton-Raphson Method (WNRM), an innovative optimization technique, is introduced in statistical supervised learning for categorization and applied to a diabetes predictive model, to find maximum likelihood estimates. The iterative optimization method solves nonlinear systems of equations with singular Jacobian matrices and is a modification of the ordinary Newton-Raphson algorithm. The quadratic convergence of the WNRM, and high efficiency for optimizing nonlinear likelihood functions, whenever singularity in the Jacobians occur allow for an easy inclusion to classical categorization and generalized linear models such as the Logistic Regression model in supervised learning. The WNRM is thoroughly investigated …
Difference Of Facial Achromatic Numbers Between Two Triangular Embeddings Of A Graph, Kengo Enami, Yumiko Ohno
Difference Of Facial Achromatic Numbers Between Two Triangular Embeddings Of A Graph, Kengo Enami, Yumiko Ohno
Theory and Applications of Graphs
A facial $3$-complete $k$-coloring of a triangulation $G$ on a surface is a vertex $k$-coloring such that every triple of $k$-colors appears on the boundary of some face of $G$. The facial $3$-achromatic number $\psi_3(G)$ of $G$ is the maximum integer $k$ such that $G$ has a facial $3$-complete $k$-coloring. This notion is an expansion of the complete coloring, that is, a proper vertex coloring of a graph such that every pair of colors appears on the ends of some edge.
For two triangulations $G$ and $G'$ on a surface, $\psi_3(G)$ may not be equal to $\psi_3(G')$ even if $G$ …
The Ricci Curvature On Simplicial Complexes, Taiki Yamada
The Ricci Curvature On Simplicial Complexes, Taiki Yamada
Theory and Applications of Graphs
We define the Ricci curvature on simplicial complexes modifying the definition of the Ricci curvature on graphs, and prove upper and lower bounds of the Ricci curvature. These properties are generalizations of previous studies. Moreover, we obtain an estimate of the eigenvalues of the Laplacian on simplicial complexes by the Ricci curvature.
Toughness Of Recursively Partitionable Graphs, Calum Buchanan, Brandon Du Preez, K. E. Perry, Puck Rombach
Toughness Of Recursively Partitionable Graphs, Calum Buchanan, Brandon Du Preez, K. E. Perry, Puck Rombach
Theory and Applications of Graphs
A simple graph G = (V,E) on n vertices is said to be recursively partitionable (RP) if G ≃ K1, or if G is connected and satisfies the following recursive property: for every integer partition a1, a2, . . . , ak of n, there is a partition {A1,A2, . . . ,Ak} of V such that each |Ai| = ai, and each induced subgraph G[Ai] is RP (1 ≤ i ≤ k). We show that if S is a …
Wiener Index In Graphs Given Girth, Minimum, And Maximum Degrees, Fadekemi J. Osaye, Liliek Susilowati, Alex S. Alochukwu, Cadavious Jones
Wiener Index In Graphs Given Girth, Minimum, And Maximum Degrees, Fadekemi J. Osaye, Liliek Susilowati, Alex S. Alochukwu, Cadavious Jones
Theory and Applications of Graphs
Let $G$ be a connected graph of order $n$. The Wiener index $W(G)$ of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. The well-known upper bound $\big( \frac{n}{\delta+1}+2\big) {n \choose 2}$ on the Wiener index of a graph of order $n$ and minimum degree $\delta$ by Kouider and Winkler \cite{Kouider} was improved significantly by Alochukwu and Dankelmann \cite{Alex} for graphs containing a vertex of large degree $\Delta$ to $W(G) \leq {n-\Delta+\delta \choose 2} \big( \frac{n+2\Delta}{\delta+1}+4 \big)$. In this paper, we give upper bounds on the Wiener index of $G$ in terms of order …
On The Hardness Of The Balanced Connected Subgraph Problem For Families Of Regular Graphs, Harsharaj Pathak
On The Hardness Of The Balanced Connected Subgraph Problem For Families Of Regular Graphs, Harsharaj Pathak
Theory and Applications of Graphs
The Balanced Connected Subgraph problem (BCS) was introduced by Bhore et al. In the BCS problem we are given a vertex-colored graph G = (V, E) where each vertex is colored “red” or “blue”. The goal is to find a maximum cardinality induced connected subgraph H of G such that H contains an equal number of red and blue vertices. This problem is known to be NP-hard for general graphs as well as many special classes of graphs. In this work we explore the time complexity of the BCS problem in case of regular graphs. We prove that the BCS …
On Nowhere Zero 4-Flows In Regular Matroids, Xiaofeng Wang, Taoye Zhang, Ju Zhou
On Nowhere Zero 4-Flows In Regular Matroids, Xiaofeng Wang, Taoye Zhang, Ju Zhou
Theory and Applications of Graphs
Walton and Welsh proved that if a co-loopless regular matroid M does not have a minor in {M(K(3,3)),M∗(K5)}, then M admits a nowhere zero 4-flow. Lai, Li and Poon proved that if M does not have a minor in {M(K5),M∗(K5)}, then M admits a nowhere zero 4-flow. We prove that if a co-loopless regular matroid M does not have a minor in {M((P10)¯3 ),M∗(K5)}, then M admits a nowhere zero 4-flow where (P10)¯3 is the graph obtained from the Petersen graph P10by contracting 3 edges of a perfect matching. As …
Individual Difference Correlates Of Being Sexually Unrestricted Yet Declining An Hiv Test, Nicholas S. Holtzman, Stephen W. Carden, Stacy W. Smallwood, Janice Steirn, S. Mason Garrison
Individual Difference Correlates Of Being Sexually Unrestricted Yet Declining An Hiv Test, Nicholas S. Holtzman, Stephen W. Carden, Stacy W. Smallwood, Janice Steirn, S. Mason Garrison
Department of Mathematical Sciences Faculty Publications
Which individual differences accurately predict one’s decision to get tested for human immunodeficiency virus (HIV), and do individuals who have regular short-term sex get tested at higher rates? Two studies—one lab study (total valid N = 69, with n = 20 who were tested) and one involving a student health center (valid N = 250, n = 4 who were tested)—involved participants (total valid N = 319, with n = 24 who got tested) taking a number of personality and individual difference measures, including the dark triad (Machiavellianism, narcissism, and psychopathy). Then, in both studies, participants had the opportunity to …
The Gamma-Signless Laplacian Adjacency Matrix Of Mixed Graphs, Omar Alomari, Mohammad Abudayah, Manal Ghanem
The Gamma-Signless Laplacian Adjacency Matrix Of Mixed Graphs, Omar Alomari, Mohammad Abudayah, Manal Ghanem
Theory and Applications of Graphs
The α-Hermitian adjacency matrix Hα of a mixed graph X has been recently introduced. It is a generalization of the adjacency matrix of unoriented graphs. In this paper, we consider a special case of the complex number α. This enables us to define an incidence matrix of mixed graphs. Consequently, we define a generalization of line graphs as well as a generalization of the signless Laplacian adjacency matrix of graphs. We then study the spectral properties of the gamma-signless Laplacian adjacency matrix of a mixed graph. Lastly, we characterize when the signless Laplacian adjacency matrix of …
Bounds For The Augmented Zagreb Index, Ren Qingcuo, Li Wen, Suonan Renqian, Yang Chenxu
Bounds For The Augmented Zagreb Index, Ren Qingcuo, Li Wen, Suonan Renqian, Yang Chenxu
Theory and Applications of Graphs
The augmented Zagreb index (AZI for short) of a graph G, introduced by Furtula et al. in 2010, is defined as AZI(G)= Σ vivj ∈ E(G)} (d(vi)d(vj)} {d(vi)+d(vj)-2)3, where E(G) is the edge set of G, and d(vi) denotes the degree of the vertex vi. In this paper, we give some new bounds on general connected graphs, molecular trees and triangle-free graphs.
New Diagonal Graph Ramsey Numbers Of Unicyclic Graphs, Richard M. Low, Ardak Kapbasov
New Diagonal Graph Ramsey Numbers Of Unicyclic Graphs, Richard M. Low, Ardak Kapbasov
Theory and Applications of Graphs
Grossman conjectured that R(G, G) = 2 ⋅ |V(G)| - 1, for all simple connected unicyclic graphs G of odd girth and |V(G)| ≥ 4. In this note, we prove his conjecture for various classes of G containing a triangle. In addition, new diagonal graph Ramsey numbers are calculated for some classes of simple connected unicyclic graphs of even girth.
Ts-Reconfiguration Of K-Path Vertex Covers In Caterpillars For K \Geq 4, Duc A. Hoang
Ts-Reconfiguration Of K-Path Vertex Covers In Caterpillars For K \Geq 4, Duc A. Hoang
Theory and Applications of Graphs
A k-path vertex cover (k-PVC) of a graph G is a vertex subset I such that each path on k vertices in G contains at least one member of I. Imagine that a token is placed on each vertex of a k-PVC. Given two k-PVCs I, J of a graph G, thek-Path Vertex Cover Reconfiguration (k-PVCR)} under Token Sliding (TS) problem asks if there is a sequence of k-PVCs between I and J where each intermediate member is obtained from its predecessor by sliding a token from some …
Ramsey Numbers For Connected 2-Colorings Of Complete Graphs, Mark Budden
Ramsey Numbers For Connected 2-Colorings Of Complete Graphs, Mark Budden
Theory and Applications of Graphs
In 1978, David Sumner introduced a variation of Ramsey numbers by restricting to 2-colorings in which the subgraphs spanned by edges in each color are connected. This paper continues the study of connected Ramsey numbers, including the evaluation of several cases of trees versus complete graphs.
A Graphical User Interface Using Spatiotemporal Interpolation To Determine Fine Particulate Matter Values In The United States, Kelly M. Entrekin
A Graphical User Interface Using Spatiotemporal Interpolation To Determine Fine Particulate Matter Values In The United States, Kelly M. Entrekin
Honors College Theses
Fine particulate matter or PM2.5 can be described as a pollution particle that has a diameter of 2.5 micrometers or smaller. These pollution particle values are measured by monitoring sites installed across the United States throughout the year. While these values are helpful, a lot of areas are not accounted for as scientists are not able to measure all of the United States. Some of these unmeasured regions could be reaching high PM2.5 values over time without being aware of it. These high values can be dangerous by causing or worsening health conditions, such as cardiovascular and lung diseases. Within …
K-8 Preservice Teachers’ Statistical Thinking When Determining Best Measure Of Center, Ha Nguyen, Eryn M. Stehr Maher, Gregory Chamblee, Sharon Taylor
K-8 Preservice Teachers’ Statistical Thinking When Determining Best Measure Of Center, Ha Nguyen, Eryn M. Stehr Maher, Gregory Chamblee, Sharon Taylor
Department of Mathematical Sciences Faculty Publications
The purpose of this study was to determine K-8 preservice teacher (PST) candidates’ statistical thinking when selecting the best center representation for the given data. Forty-four PSTs enrolled in a Statistics and Probability for K-8 Teachers course in a university located in the southeastern region of the United States were asked to complete a 2007 National Assessment of Educational Progress test item. All 44 PSTs’ data were qualitatively analyzed for correctness and statistical thinking strategies used. Findings were that most PSTs either incorrectly selected the mean, rather than median, as the best measure of center for the given data or …
Optimal Orientations Of Vertex-Multiplications Of Trees With Diameter 4, Willie Han Wah Wong, Eng Guan Tay
Optimal Orientations Of Vertex-Multiplications Of Trees With Diameter 4, Willie Han Wah Wong, Eng Guan Tay
Theory and Applications of Graphs
Koh and Tay proved a fundamental classification of G vertex-multiplications into three classes ζ0, ζ1 and ζ2. They also showed that any vertex-multiplication of a tree with diameter at least 3 does not belong to the class ζ2. Of interest, G vertex-multiplications are extensions of complete n-partite graphs and Gutin characterised complete bipartite graphs with orientation number 3 (or 4 resp.) via an ingenious use of Sperner's theorem. In this paper, we investigate vertex-multiplications of trees with diameter 4 in ζ0 (or ζ1) and exhibit its intricate connections with …
Outer Independent Double Italian Domination Of Some Graph Products, Rouhollah Jalaei, Doost Ali Mojdeh
Outer Independent Double Italian Domination Of Some Graph Products, Rouhollah Jalaei, Doost Ali Mojdeh
Theory and Applications of Graphs
An outer independent double Italian dominating function on a graph G is a function f:V(G) →{0,1,2,3} for which each vertex x ∈ V(G) with {f(x)∈ {0,1} then Σy ∈ N[x]f(y) ⩾ 3 and vertices assigned 0 under f are independent. The outer independent double Italian domination number γoidI(G) is the minimum weight of an outer independent double Italian dominating function of graph G. In this work, we present some contributions to the study of outer independent double Italian domination of three graph products. We characterize the Cartesian product, lexicographic product and direct product of custom …
Counting Power Domination Sets In Complete M-Ary Trees, Hays Whitlatch, Katharine Shultis, Olivia Ramirez, Michele Ortiz, Sviatlana Kniahnitskaya
Counting Power Domination Sets In Complete M-Ary Trees, Hays Whitlatch, Katharine Shultis, Olivia Ramirez, Michele Ortiz, Sviatlana Kniahnitskaya
Theory and Applications of Graphs
Motivated by the question of computing the probability of successful power domination by placing k monitors uniformly at random, in this paper we give a recursive formula to count the number of power domination sets of size k in a labeled complete m-ary tree. As a corollary we show that the desired probability can be computed in exponential with linear exponent time.
Hs-Integral And Eisenstein Integral Mixed Circulant Graphs, Monu Kadyan, Bikash Bhattacharjya
Hs-Integral And Eisenstein Integral Mixed Circulant Graphs, Monu Kadyan, Bikash Bhattacharjya
Theory and Applications of Graphs
A mixed graph is called second kind hermitian integral (HS-integral) if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers. A mixed graph is called Eisenstein integral if the eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. We characterize the set S for which a mixed circulant graph Circ(Zn, S) is HS-integral. We also show that a mixed circulant graph is Eisenstein integral if and only if it is HS-integral. Further, we express the eigenvalues and the HS-eigenvalues of unitary oriented circulant graphs in terms of generalized Möbius function.
On The Uniqueness Of Continuation Of A Partially Defined Metric, Evgeniy Petrov
On The Uniqueness Of Continuation Of A Partially Defined Metric, Evgeniy Petrov
Theory and Applications of Graphs
The problem of continuation of a partially defined metric can be efficiently studied using graph theory. Let G=G(V,E) be an undirected graph with the set of vertices V and the set of edges E. A necessary and sufficient condition under which the weight w : E → R+ on the graph G has a unique continuation to a metric d : V x V → R+ is found.
On Rainbow Cycles And Proper Edge Colorings Of Generalized Polygons, Matt Noble
On Rainbow Cycles And Proper Edge Colorings Of Generalized Polygons, Matt Noble
Theory and Applications of Graphs
An edge coloring of a simple graph G is said to be proper rainbow-cycle-forbidding (PRCF, for short) if no two incident edges receive the same color and for any cycle in G, at least two edges of that cycle receive the same color. A graph G is defined to be PRCF-good if it admits a PRCF edge coloring, and G is deemed PRCF-bad otherwise. In recent work, Hoffman, et al. study PRCF edge colorings and find many examples of PRCF-bad graphs having girth less than or equal to 4. They then ask whether such graphs exist having girth greater than …
Supporting Spatial Reasoning: Identifying Aspects Of Length, Area, And Volume In Textbook Definitions, Eryn M. Stehr Maher, Jia He
Supporting Spatial Reasoning: Identifying Aspects Of Length, Area, And Volume In Textbook Definitions, Eryn M. Stehr Maher, Jia He
Department of Mathematical Sciences Faculty Publications
Length, area, and volume share structural similarities enabling flexibility in reasoning for real-world applications. Deep understanding of structures can help teachers connect these concepts to support their students’ mathematical reasoning and practices involving real-world situations. In mathematics textbooks designed for future teachers, definitions of length, area, and volume vary from procedural (e.g., use a ruler to measure side lengths, use formulas to calculate measures) to conceptual (e.g., construct appropriate n-dimensional units that tessellate the n-dimensional space) to formal (e.g., construct a function mapping qualitative size to a quantity of appropriate units). Most textbooks describe length, area, and volume …
Path-Stick Solitaire On Graphs, Jan-Hendrik De Wiljes, Martin Kreh
Path-Stick Solitaire On Graphs, Jan-Hendrik De Wiljes, Martin Kreh
Theory and Applications of Graphs
In 2011, Beeler and Hoilman generalised the game of peg solitaire to arbitrary connected graphs. Since then, peg solitaire and related games have been considered on many graph classes. In this paper, we introduce a variant of the game peg solitaire, called path-stick solitaire, which is played with sticks in edges instead of pegs in vertices. We prove several analogues to peg solitaire results for that game, mainly regarding different graph classes. Furthermore, we characterise, with very few exceptions, path-stick-solvable joins of graphs and provide some possible future research questions.
Embrace Cultural Relevance With Mathematical Decision-Making, Jordan Moreno, Eryn M. Maher
Embrace Cultural Relevance With Mathematical Decision-Making, Jordan Moreno, Eryn M. Maher
College of Science and Mathematics Faculty Presentations
We share and implement a multi-step strategy for adapting tasks by opening contexts to student decisionmaking and exploration