Open Access. Powered by Scholars. Published by Universities.®
- Institution
-
- Brigham Young University (5)
- Prairie View A&M University (4)
- Rose-Hulman Institute of Technology (4)
- Utah State University (4)
- Missouri State University (3)
-
- TÜBİTAK (3)
- University of Tennessee, Knoxville (3)
- Claremont Colleges (2)
- Louisiana State University (2)
- University of Mississippi (2)
- University of Vermont (2)
- Bard College (1)
- City University of New York (CUNY) (1)
- Clemson University (1)
- Georgia Southern University (1)
- Illinois State University (1)
- Marshall University (1)
- Murray State University (1)
- Pepperdine University (1)
- Selected Works (1)
- The College of Wooster (1)
- University of Al-Qadisiyah (1)
- University of Connecticut (1)
- University of New Mexico (1)
- University of South Carolina (1)
- University of Texas Rio Grande Valley (1)
- University of Texas at Tyler (1)
- West Virginia University (1)
- Wilfrid Laurier University (1)
- Zayed University (1)
- Publication Year
- Publication
-
- Theses and Dissertations (8)
- Applications and Applied Mathematics: An International Journal (AAM) (4)
- MSU Graduate Theses (3)
- Rose-Hulman Undergraduate Mathematics Journal (3)
- Turkish Journal of Mathematics (3)
-
- Doctoral Dissertations (2)
- Electronic Theses and Dissertations (2)
- Graduate College Dissertations and Theses (2)
- LSU Doctoral Dissertations (2)
- Al-Qadisiyah Journal of Pure Science (1)
- All Graduate Plan B and other Reports, Spring 1920 to Spring 2023 (1)
- All Graduate Theses and Dissertations, Spring 1920 to Summer 2023 (1)
- All Theses (1)
- All Works (1)
- Branch Mathematics and Statistics Faculty and Staff Publications (1)
- Browse All Undergraduate research (1)
- Carl Mummert (1)
- Dissertations, Theses, and Capstone Projects (1)
- Graduate Theses, Dissertations, and Problem Reports (1)
- HMC Senior Theses (1)
- Honors College Theses (1)
- Honors Scholar Theses (1)
- Journal of Humanistic Mathematics (1)
- Masters Theses (1)
- Math Theses (1)
- Mathematical Sciences Technical Reports (MSTR) (1)
- Mathematics Faculty Research (1)
- Seaver College Research And Scholarly Achievement Symposium (1)
- Senior Independent Study Theses (1)
- Senior Projects Spring 2018 (1)
- Publication Type
Articles 1 - 30 of 53
Full-Text Articles in Entire DC Network
Some Generalizations Of Corona Product Of Two Graphs, Aparajita Borah, Gajendra Pratap Singh
Some Generalizations Of Corona Product Of Two Graphs, Aparajita Borah, Gajendra Pratap Singh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we are seeking to conceptualize the notion of corona product of two graphs to contrive some special types of graphs. That is, here our attempt is to regenerate a familiar graph as a product graph. We are considering seven familiar graphs here to reconstruct them with the help of corona product of two graphs. Such types of families of the graphs and operations can be used to study biological pathways as well as to find the optimal order and size for the special types of graphs.
Edge Colored And Edge Ordered Graphs, Per Gustin Wagenius
Edge Colored And Edge Ordered Graphs, Per Gustin Wagenius
Graduate College Dissertations and Theses
In this work, the current state of the field of edge-colored graphs is surveyed. Anew concept of unshrinkable edge colorings is introduced which is useful for rainbow subgraph problems and interesting in its own right. This concept is analyzed in some depth. Building upon the linear edge ordering described in a recent work from Gerbner, Methuku, Nagy, Pálvölgyi, Tardos, and Vizer, edge-ordering graphs with the cyclic group is introduced and some results are given on this and a related counting problem.
Strategies Community College Mexican American Adult College Algebra Students Use When Graphing Function Transformations, Roxana Pamela Jimenez
Strategies Community College Mexican American Adult College Algebra Students Use When Graphing Function Transformations, Roxana Pamela Jimenez
Theses and Dissertations
This qualitative case study pursued to describe the different strategies Mexican American adult students in a local community college used to graph function transformations. Participants in the study were purposefully selected using a criterion sampling to ensure participants were atypical, above average students between the ages 18-22, and had a final course average of 89.5-100 in College Algebra. Three research questions were examined 1) In what ways do Mexican American adult college students graph a function transformation? 2) Which strategies do students implement when graphing a function transformation? Qualitative research methods using think aloud semi-structured interviews were used in this …
Structure Of A Total Independent Set, Lewis Stanton
Structure Of A Total Independent Set, Lewis Stanton
Rose-Hulman Undergraduate Mathematics Journal
Let $G$ be a simple, connected and finite graph with order $n$. Denote the independence number, edge independence number and total independence number by $\alpha(G), \alpha'(G)$ and $\alpha''(G)$ respectively. This paper establishes an upper bound for $\alpha''(G)$ in terms of $\alpha(G)$, $\alpha'(G)$ and $n$. We also describe the possible structures for a total independent set containing a given number of elements.
Cohen-Macaulay Properties Of Closed Neighborhood Ideals, Jackson Leaman
Cohen-Macaulay Properties Of Closed Neighborhood Ideals, Jackson Leaman
All Theses
This thesis investigates Cohen-Macaulay properties of squarefree monomial ideals, which is an important line of inquiry in the field of combinatorial commutative algebra. A famous example of this is Villareal’s edge ideal [11]: given a finite simple graph G with vertices x1, . . . , xn, the edge ideal of G is generated by all the monomials of the form xixj where xi and xj are adjacent in G. Villareal’s characterization of Cohen-Macaulay edge ideals associated to trees is an often-cited result in the literature. This was extended to chordal and bipartite graphs by Herzog, Hibi, and Zheng in …
Matroid Generalizations Of Some Graph Results, Cameron Crenshaw
Matroid Generalizations Of Some Graph Results, Cameron Crenshaw
LSU Doctoral Dissertations
The edges of a graph have natural cyclic orderings. We investigate the matroids for which a similar cyclic ordering of the circuits is possible. A full characterization of the non-binary matroids with this property is given. Evidence of the difficulty of this problem for binary matroids is presented, along with a partial result for binary orderable matroids.
For a graph G, the ratio of |E(G)| to the minimum degree of G has a natural lower bound. For a matroid M that is representable over a finite field, we generalize this to a lower bound on …
Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic
Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic
Turkish Journal of Mathematics
This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph, and the last is the graph-associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs. In the last section, we study some properties related to $\mathcal{H}$-polytopes.
Supra-Approximation Spaces Using Combined Edges Systems, Hussein R. Jaffer, Khalid Sh. Al’Dzhabri
Supra-Approximation Spaces Using Combined Edges Systems, Hussein R. Jaffer, Khalid Sh. Al’Dzhabri
Al-Qadisiyah Journal of Pure Science
The primary in this paper's notion, the i-space using incident edges system (resp. n-space using non-incidental edges system), is what this study is responsible for generating and investigating. Additionally, we used c-interior to define the c-lower approximations in generalized rough set theory (resp. i-interior and n-interior) Additionally, the c-upper approximations are defined using c-closure (as opposed to i-closure and n-closure), and some of its characteristics are studied.
2-Uniform Covering Groups Of Elementary Abelian 2-Groups, Dana Saleh, Rachel Quinlan
2-Uniform Covering Groups Of Elementary Abelian 2-Groups, Dana Saleh, Rachel Quinlan
All Works
This article is concerned with the classification of Schur covering groups of the elementary abelian group of order (Formula presented.), up to isomorphism. We consider those covering groups possessing a generating set of n elements having only two distinct squares. We show that such groups may be represented by 2-vertex-colored and 2-edge-colored graphs of order n. We show that in most cases, the isomorphism type of the group is determined by that of the 2-colored graph, and we analyze the exceptions.
Opposite Trees, Theo Goossens
Opposite Trees, Theo Goossens
Theses and Dissertations (Comprehensive)
A spanning tree of a graph G is a connected acyclic subgraph of G that includes all of the vertices in G. The degree of a vertex is the number of edges incident to that vertex. Given a spanning tree T of a graph G, an opposite tree of T is a spanning tree of G where the degree of each of its vertices is different from its degree in T. For complete, complete bipartite, and complete multipartite graphs, we give the conditions spanning trees of these graphs must satisfy in order to have an opposite tree.
Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram
Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram
Journal of Humanistic Mathematics
Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and …
Quantum Dimension Polynomials: A Networked-Numbers Game Approach, Nicholas Gaubatz
Quantum Dimension Polynomials: A Networked-Numbers Game Approach, Nicholas Gaubatz
Honors College Theses
The Networked-Numbers Game--a mathematical "game'' played on a simple graph--is incredibly accessible and yet surprisingly rich in content. The Game is known to contain deep connections to the finite-dimensional simple Lie algebras over the complex numbers. On the other hand, Quantum Dimension Polynomials (QDPs)--enumerative expressions traditionally understood through root systems--corresponding to the above Lie algebras are complicated to derive and often inaccessible to undergraduates. In this thesis, the Networked-Numbers Game is defined and some known properties are presented. Next, the significance of the QDPs as a method to count combinatorially interesting structures is relayed. Ultimately, a novel closed-form expression of …
Minimal Inscribed Polyforms, Jack Hanke
Minimal Inscribed Polyforms, Jack Hanke
Honors Scholar Theses
A polyomino of size n is constructed by joining n unit squares together by their edge to form a shape in the plane. This thesis will first examine the formal definition of a polyomino and the common equivalence classes polyominos are enumerated under. We then turn to polyomino families, and provide exact enumeration results for certain families, including the minimal inscribed polyominos. Next we will generalize polyominos to polyforms, and provide novel formulae for polyform analogues of minimal inscribed polyominos. Finally, we discuss some further questions concerning minimal inscribed polyforms.
On The Hamiltonicity Of Subgroup Lattices, Nicholas Charles Fleece
On The Hamiltonicity Of Subgroup Lattices, Nicholas Charles Fleece
MSU Graduate Theses
In this paper we discuss the Hamiltonicity of the subgroup lattices of
different classes of groups. We provide sufficient conditions for the
Hamiltonicity of the subgroup lattices of cube-free abelian groups. We also
prove the non-Hamiltonicity of the subgroup lattices of dihedral and
dicyclic groups. We disprove a conjecture on non-abelian p-groups by
producing an infinite family of non-abelian p-groups with Hamiltonian
subgroup lattices. Finally, we provide a list of the Hamiltonicity of the
subgroup lattices of every finite group up to order 35 barring two groups.
Proper Sum Graphs, Austin Nicholas Beard
Proper Sum Graphs, Austin Nicholas Beard
MSU Graduate Theses
The Proper Sum Graph of a commutative ring with identity has the prime ideals as vertices, with two ideals adjacent if their sum is a proper ideal. This thesis expands upon the research of Dhorajia. We will cover the groundwork to understanding the basics of these graphs, and gradually narrow our efforts into the minimal prime ideals of the ring.
Exponents Of Jacobians Of Graphs And Regular Matroids, Hahn Lheem, Deyuan Li, Carl Joshua Quines, Jessica Zhang
Exponents Of Jacobians Of Graphs And Regular Matroids, Hahn Lheem, Deyuan Li, Carl Joshua Quines, Jessica Zhang
Rose-Hulman Undergraduate Mathematics Journal
Let G be a finite undirected multigraph with no self-loops. The Jacobian Jac (G) is a finite abelian group associated with G whose cardinality is equal to the number of spanning trees of G. There are only a finite number of biconnected graphs G such that the exponent of Jac (G) equals 2 or 3. The definition of a Jacobian can also be extended to regular matroids as a generalization of graphs. We prove that there are finitely many connected regular matroids M such that Jac (M) has exponent 2 and characterize all such matroids.
Jacobians Of Finite And Infinite Voltage Covers Of Graphs, Sophia Rose Gonet
Jacobians Of Finite And Infinite Voltage Covers Of Graphs, Sophia Rose Gonet
Graduate College Dissertations and Theses
The Jacobian group (also known as the critical group or sandpile group) is an important invariant of a graph X; it is a finite abelian group whose cardinality is equal to the number of spanning trees of X (Kirchhoff's Matrix Tree Theorem). This dissertation proves results about the Jacobians of certain families of covering graphs, Y, of a base graph X, that are constructed from an assignment of elements from a group G to the edges of X (G is called the voltage group and Y is called the derived graph). The principal aim is to relate the Jacobian of …
Logarithmic Mean Labeling Of Some Ladder Related Graphs, A. Durai Baskar
Logarithmic Mean Labeling Of Some Ladder Related Graphs, A. Durai Baskar
Applications and Applied Mathematics: An International Journal (AAM)
In general, the logarithmic mean of two positive integers need not be an integer. Hence, the logarithmic mean is to be an integer; we use either flooring or ceiling function. The logarithmic mean labeling of graphs have been defined in which the edge labels may be assigned by either flooring function or ceiling function. In this, we establish the logarithmic mean labeling on graphs by considering the edge labels obtained only from the flooring function. A logarithmic mean labeling of a graph G with q edges is an injective function from the vertex set of G to 1, 2, 3,..., …
The Game Of Cops And Robbers On Planar Graphs, Jordon S. Daugherty
The Game Of Cops And Robbers On Planar Graphs, Jordon S. Daugherty
MSU Graduate Theses
In graph theory, the game of cops and robbers is played on a finite, connected graph. The players take turns moving along edges as the cops try to capture the robber and the robber tries to evade capture forever. This game has received quite a bit of recent attention including several conjectures that have yet to be proven. In this paper, we restricted our attention to planar graphs in order to try to prove the conjecture that the dodecahedron graph is the smallest planar graph, in terms of vertices, that has cop number three. Along the way we discuss several …
Demystification Of Graph And Information Entropy, Bryce Frederickson
Demystification Of Graph And Information Entropy, Bryce Frederickson
Undergraduate Honors Capstone Projects
Shannon entropy is an information-theoretic measure of unpredictability in probabilistic models. Recently, it has been used to form a tool, called the von Neumann entropy, to study quantum mechanics and network flows by appealing to algebraic properties of graph matrices. But still, little is known about what the von Neumann entropy says about the combinatorial structure of the graphs themselves. This paper gives a new formulation of the von Neumann entropy that describes it as a rate at which random movement settles down in a graph. At the same time, this new perspective gives rise to a generalization of von …
Consecutive Prime And Highly Total Prime Labeling In Graphs, Robert Scholle
Consecutive Prime And Highly Total Prime Labeling In Graphs, Robert Scholle
Rose-Hulman Undergraduate Mathematics Journal
This paper examines the graph-theoretical concepts of consecutive prime labeling and highly total prime labeling. These are variations on prime labeling, introduced by Tout, Dabboucy, and Howalla in 1982. Consecutive prime labeling is defined here for the first time. Consecutive prime labeling requires that the labels of vertices in a graph be relatively prime to the labels of all adjacent vertices as well as all incident edges. We show that all paths, cycles, stars, and complete graphs have a consecutive prime labeling and conjecture that all simple connected graphs have a consecutive prime labeling.
This paper also expands on work …
A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler
A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler
Senior Independent Study Theses
Santorini is a two player combinatorial board game. Santorini bears resemblance to the graph theory game of Geography, a game of moving and deleting vertices on a graph. We explore Santorini with game theory, complexity theory, and artificial intelligence. We present David Lichtenstein’s proof that Geography is PSPACE-hard and adapt the proof for generalized forms of Santorini. Last, we discuss the development of an AI built for a software implementation of Santorini and present a number of improvements to that AI.
Jones Polynomial For Graphs Of Twist Knots, Abdulgani Şahin, Bünyamin Şahin
Jones Polynomial For Graphs Of Twist Knots, Abdulgani Şahin, Bünyamin Şahin
Applications and Applied Mathematics: An International Journal (AAM)
We frequently encounter knots in the flow of our daily life. Either we knot a tie or we tie a knot on our shoes. We can even see a fisherman knotting the rope of his boat. Of course, the knot as a mathematical model is not that simple. These are the reflections of knots embedded in threedimensional space in our daily lives. In fact, the studies on knots are meant to create a complete classification of them. This has been achieved for a large number of knots today. But we cannot say that it has been terminated yet. There are …
Reverse Mathematics Of Matroids, Jeffry L. Hirst, Carl Mummert
Reverse Mathematics Of Matroids, Jeffry L. Hirst, Carl Mummert
Carl Mummert
Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basis theorems for matroids and enumerated matroids. Next, using Weihrauch reducibility, we relate the basis results to combinatorial choice principles and statements about vector spaces. Finally, we formalize some of the Weihrauch reductions to extract related reverse mathematics results. In particular, we show that the existence of bases for vector spaces of bounded dimension is equivalent to the induction scheme for \Sigma^0_2 formulas.
On Fractional Realizations Of Tournament Score Sequences, Kaitlin S. Murphy
On Fractional Realizations Of Tournament Score Sequences, Kaitlin S. Murphy
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Contrary to popular belief, we can’t all be winners.
Suppose 6 people compete in a chess tournament in which all pairs of players compete directly and no ties are allowed; i.e., 6 people compete in a ‘round robin tournament’. Each player is assigned a ‘score’, namely the number of games they won, and the ‘score sequence’ of the tournament is a list of the players’ scores. Determining whether a given potential score sequence actually is a score sequence proves to be difficult. For instance, (0, 0, 3, 3, 3, 6) is not feasible because two players cannot both have …
The Knill Graph Dimension From Clique Cover, Evatt Salinger, Dr. Kassahun Betre
The Knill Graph Dimension From Clique Cover, Evatt Salinger, Dr. Kassahun Betre
Seaver College Research And Scholarly Achievement Symposium
In this paper we prove that the recursive (Knill) dimension of the join of two graphs has a simple formula in terms of the dimensions of the component graphs: dim (G1 + G2) = 1 + dim G1 + dim G2. We use this formula to derive an expression for the Knill dimension of a graph from its minimum clique cover. A corollary of the formula is that a graph made of the arbitrary union of complete graphs KN of the same order KN will have dimension N − 1.
Finite Simple Graphs And Their Associated Graph Lattices, James B. Hart, Brian Frazier
Finite Simple Graphs And Their Associated Graph Lattices, James B. Hart, Brian Frazier
Theory and Applications of Graphs
In his 2005 dissertation, Antoine Vella explored combinatorical aspects of finite graphs utilizing a topological space whose open sets are intimately tied to the structure of the graph. In this paper, we go a step further and examine some aspects of the open set lattices induced by these topological spaces. In particular, we will characterize all lattices that constitute the opens for finite simple graphs endowed with this topology, explore the structure of these lattices, and show that these lattices contain information necessary to reconstruct the graph and its complement in several ways.
Unavoidable Immersions And Intertwines Of Graphs, Matthew Christopher Barnes
Unavoidable Immersions And Intertwines Of Graphs, Matthew Christopher Barnes
LSU Doctoral Dissertations
The topological minor and the minor relations are well-studied binary relations on the class of graphs. A natural weakening of the topological minor relation is an immersion. An immersion of a graph H into a graph G is a map that injects the vertex set of H into the vertex set of G such that edges between vertices of H are represented by pairwise-edge-disjoint paths of G. In this dissertation, we present two results: the first giving a set of unavoidable immersions of large 3-edge-connected graphs and the second on immersion intertwines of infinite graphs. These results, along with …
On Some Geometry Of Graphs, Zachary S. Mcguirk
On Some Geometry Of Graphs, Zachary S. Mcguirk
Dissertations, Theses, and Capstone Projects
In this thesis we study the intrinsic geometry of graphs via the constants that appear in discretized partial differential equations associated to those graphs. By studying the behavior of a discretized version of Bochner's inequality for smooth manifolds at the cone point for a cone over the set of vertices of a graph, a lower bound for the internal energy of the underlying graph is obtained. This gives a new lower bound for the size of the first non-trivial eigenvalue of the graph Laplacian in terms of the curvature constant that appears at the cone point and the size of …
Exploring Sequences Of Tournament Graphs With Draws, Kaylynn H. Tran
Exploring Sequences Of Tournament Graphs With Draws, Kaylynn H. Tran
Senior Projects Spring 2018
Tournaments occur all over the world and they are used to decide championships in various competitions. For this project, I will be exploring tournaments in the round robin style in which every team plays one another. This is based on Sadiki Lewis' senior project, Exploring Tournament Graphs and Their Win Sequences. I will be expanding his project by including the possibility of a draw between two teams, in addition to a win or a loss. Teams and games will be modeled by complete graphs where each vertex represents a team and each directed edge between two vertices represents the outcome …