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Articles 1  30 of 1115
FullText Articles in Discrete Mathematics and Combinatorics
Counting Power Domination Sets In Complete MAry Trees, Hays Whitlatch, Katharine Shultis, Olivia Ramirez, Michele Ortiz, Sviatlana Kniahnitskaya
Counting Power Domination Sets In Complete MAry 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 mary tree. As a corollary we show that the desired probability can be computed in exponential with linear exponent time.
HsIntegral And Eisenstein Integral Mixed Circulant Graphs, Monu Kadyan, Bikash Bhattacharjya
HsIntegral And Eisenstein Integral Mixed Circulant Graphs, Monu Kadyan, Bikash Bhattacharjya
Theory and Applications of Graphs
A mixed graph is called \emph{second kind hermitian integral} (\emph{HSintegral}) if the eigenvalues of its Hermitianadjacency matrix of the second kind are integers. A mixed graph is called \emph{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 $\text{Circ}(\mathbb{Z}_n, S)$ is HSintegral. We also show that a mixed circulant graph is Eisenstein integral if and only if it is HSintegral. Further, we express the eigenvalues and the HSeigenvalues of unitary oriented circulant graphs in terms of generalized M$\ddot{\text{o}}$bius function.
Algorithmic Methods For Covering Arrays Of Higher Index, Ryan Dougherty, Kristoffer Kleine, Michael Wagner, Charles J. Colbourn, Dimitris E. Simos
Algorithmic Methods For Covering Arrays Of Higher Index, Ryan Dougherty, Kristoffer Kleine, Michael Wagner, Charles J. Colbourn, Dimitris E. Simos
West Point Research Papers
Covering arrays are combinatorial objects used in testing largescale systems to increase confidence in their correctness. To do so, each interaction of at most a specified number t of factors is represented in at least one test; that is, the covering array has strength t and index 1. For certain systems, the outcome of running a test may be altered by variability of the interaction effect or by measurement error of the test result. To improve the efficacy of testing, one can ensure that each interaction of t or fewer factors is represented in at least λ tests. When λ …
Meertens Number And Its Variations, Chai Wah Wu
Meertens Number And Its Variations, Chai Wah Wu
Communications on Number Theory and Combinatorial Theory
In 1998, Bird introduced Meertens numbers as numbers that are invariant under a map similar to the Gödel encoding. In base 10, the only known Meertens number is 81312000. We look at some properties of Meertens numbers and consider variations of this concept. In particular, we consider variations of Meertens numbers where there is a finite time algorithm to decide whether such numbers exist, exhibit infinite families of these variations and provide bounds on parameters needed for their existence.
(R1979) Permanent Of ToeplitzHessenberg Matrices With Generalized Fibonacci And Lucas Entries, Hacène Belbachir, Amine Belkhir, IhabEddine Djellas
(R1979) Permanent Of ToeplitzHessenberg Matrices With Generalized Fibonacci And Lucas Entries, Hacène Belbachir, Amine Belkhir, IhabEddine Djellas
Applications and Applied Mathematics: An International Journal (AAM)
In the present paper, we evaluate the permanent and determinant of some ToeplitzHessenberg matrices with generalized Fibonacci and generalized Lucas numbers as entries.We develop identities involving sums of products of generalized Fibonacci numbers and generalized Lucas numbers with multinomial coefficients using the matrix structure, and then we present an application of the determinant of such matrices.
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 rainbowcycleforbidding (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 PRCFgood if it admits a PRCF edge coloring, and G is deemed PRCFbad otherwise. In recent work, Hoffman, et al. study PRCF edge colorings and find many examples of PRCFbad graphs having girth less than or equal to 4. They then ask whether such graphs exist having girth greater than …
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 $w\colon E\to\mathbb R^+$ on the graph $G$ has a unique continuation to a metric $d\colon V\times V\to\mathbb R^+$ is found.
Extension Of Fundamental Transversals And Euler’S Polyhedron Theorem, Joy Marie D'Andrea
Extension Of Fundamental Transversals And Euler’S Polyhedron Theorem, Joy Marie D'Andrea
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modularity And Boolean Network Decomposition, Matthew Wheeler
Modularity And Boolean Network Decomposition, Matthew Wheeler
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
PathStick Solitaire On Graphs, JanHendrik De Wiljes, Martin Kreh
PathStick Solitaire On Graphs, JanHendrik 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 pathstick 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, pathsticksolvable joins of graphs and provide some possible future research questions.
Combinatorial Algorithms For Graph Discovery And Experimental Design, Raghavendra K. Addanki
Combinatorial Algorithms For Graph Discovery And Experimental Design, Raghavendra K. Addanki
Doctoral Dissertations
In this thesis, we study the design and analysis of algorithms for discovering the structure and properties of an unknown graph, with applications in two different domains: causal inference and sublinear graph algorithms. In both these domains, graph discovery is possible using restricted forms of experiments, and our objective is to design lowcost experiments.
First, we describe efficient experimental approaches to the causal discovery problem, which in its simplest form, asks us to identify the causal relations (edges of the unknown graph) between variables (vertices of the unknown graph) of a given system. For causal discovery, we study algorithms …
Alpha Labeling Of Amalgamated Cycles, Christian Barrientos
Alpha Labeling Of Amalgamated Cycles, Christian Barrientos
Theory and Applications of Graphs
A graceful labeling of a bipartite graph is an \alabeling if it has the property that the labels assigned to the vertices of one stable set of the graph are smaller than the labels assigned to the vertices of the other stable set. A concatenation of cycles is a connected graph formed by a collection of cycles, where each cycle shares at most either two vertices or two edges with other cycles in the collection. In this work we investigate the existence of \alabelings for this kind of graphs, exploring the concepts of vertex amalgamation to produce a family of …
(Si10054) Nonsplit Edge Geodetic Domination Number Of A Graph, P. Arul Paul Sudhahar, J. Jeba Lisa
(Si10054) Nonsplit Edge Geodetic Domination Number Of A Graph, P. Arul Paul Sudhahar, J. Jeba Lisa
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we have defined an inventive parameter called the nonsplit edge geodetic domination number of a graph, and some of its general properties are studied. The nonsplit edge geodetic domination number of some standard graph is obtained. In this work, we also determine the realization results of the nonsplit edge geodetic domination number and the edge geodetic number of a graph.
(Si10089) Integer Cordial Labeling Of Alternate Snake Graph And Irregular Snake Graph, Pratik Shah, Dharamvirsinh Parmar
(Si10089) Integer Cordial Labeling Of Alternate Snake Graph And Irregular Snake Graph, Pratik Shah, Dharamvirsinh Parmar
Applications and Applied Mathematics: An International Journal (AAM)
If a graph G admits integer cordial labeling, it is called an integer cordial graph. In this paper we prove that Alternate mtriangular Snake graph, Quadrilateral Snake graph, Alternate m quadrilateral Snake graph, Pentagonal Snake graph, Alternate mpentagonal Snake graph, Irregular triangular Snake graph, Irregular quadrilateral Snake graph, and Irregular pentagonal Snake graphs are integer cordial graphs.
Conflict Dynamics In ScaleFree Networks With Degree Correlations And Hierarchical Structure, Eduardo JacoboVillegas, Bibiana ObregónQuintana, Lev GuzmánVargas, Larry S. Liebovitch
Conflict Dynamics In ScaleFree Networks With Degree Correlations And Hierarchical Structure, Eduardo JacoboVillegas, Bibiana ObregónQuintana, Lev GuzmánVargas, Larry S. Liebovitch
Publications and Research
We present a study of the dynamic interactions between actors located on complex networks with scalefree and hierarchical scalefree topologies with assortative mixing, that is, correlations between the degree distributions of the actors. The actor’s state evolves according to a model that considers its previous state, the inertia to change, and the influence of its neighborhood. We show that the time evolution of the system depends on the percentage of cooperative or competitive
interactions. For scalefree networks, we find that the dispersion between actors is higher when all interactions are either cooperative or competitive, while a balanced presence of interactions …
(Si10130) On Regular Inverse Eccentric Fuzzy Graphs, N. Meenal, J. Jeromi Jovita
(Si10130) On Regular Inverse Eccentric Fuzzy Graphs, N. Meenal, J. Jeromi Jovita
Applications and Applied Mathematics: An International Journal (AAM)
Two new concepts of regular inverse eccentric fuzzy graphs and totally regular inverse eccentric fuzzy graphs are established in this article. By illustrations, these two graphs are compared and the results are derived. Equivalent condition for the existence of these two graphs are found. The exact values of Order and Size for some standard inverse eccentric graphs are also derived.
Asymptotic Classes, Pseudofinite Cardinality And Dimension, Alexander Van Abel
Asymptotic Classes, Pseudofinite Cardinality And Dimension, Alexander Van Abel
Dissertations, Theses, and Capstone Projects
We explore the consequences of various modeltheoretic tameness conditions upon the behavior of pseudofinite cardinality and dimension. We show that for pseudofinite theories which are either Morley Rank 1 or uncountably categorical, pseudofinite cardinality in ultraproducts satisfying such theories is highly wellbehaved. On the other hand, it has been shown that pseudofinite dimension is not necessarily wellbehaved in all ultraproducts of theories which are simple or supersimple; we extend such an observation by constructing simple and supersimple theories in which pseudofinite dimension is necessarily illbehaved in all such ultraproducts. Additionally, we have novel results connecting various forms of asymptotic classes …
The OnLine Width Of Various Classes Of Posets., Israel R. Curbelo
The OnLine Width Of Various Classes Of Posets., Israel R. Curbelo
Electronic Theses and Dissertations
An online chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemer\'edi proved that any online algorithm could be forced to use $\binom{w+1}{2}$ chains to partition a poset of width $w$. The maximum number of chains that can be forced on any online algorithm remains unknown. In the survey paper by Bosek et al., variants of the problem were studied where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size $d$. We prove …
Minimal Differential Graded Algebra Resolutions Related To Certain StanleyReisner Rings, Todd Anthony Morra
Minimal Differential Graded Algebra Resolutions Related To Certain StanleyReisner Rings, Todd Anthony Morra
All Dissertations
We investigate algebra structures on resolutions of a special class of CohenMacaulay simplicial complexes. Given a simplicial complex, we define a pure simplicial complex called the purification. These complexes arise as a generalization of certain independence complexes and the resultant StanleyReisner rings have numerous desirable properties, e.g., they are CohenMacaulay. By realizing the purification in the context of work of D'alì, et al., we obtain a multigraded, minimal free resolution of the Alexander dual ideal of the StanleyReisner ideal. We augment this in a standard way to obtain a resolution of the quotient ring, which is likewise minimal and multigraded. …
Verifying Sudoku Puzzles, Chelsea Schweer
Verifying Sudoku Puzzles, Chelsea Schweer
Electronic Theses, Projects, and Dissertations
Sudoku puzzles, created by Meki Kaji around 1983, consist of a square 9 by 9 grid made up of 9 rows, 9 columns, and nine 3 by 3 square subgrids called blocks. The goal of the puzzle is to be able to place the numbers 1 through 9 in every row, column, and block where no number is repeated in each row, column, and block. Imagine being given a completed Sudoku puzzle and having to check that it was solved correctly. You could just check all the rows columns and blocks (27 items), but is there a smaller number of …
Characteristic Sets Of Matroids, Dony Varghese
Characteristic Sets Of Matroids, Dony Varghese
Doctoral Dissertations
Matroids are combinatorial structures that generalize the properties of linear independence. But not all matroids have linear representations. Furthermore, the existence of linear representations depends on the characteristic of the fields, and the linear characteristic set is the set of characteristics of fields over which a matroid has a linear representation. The algebraic independence in a field extension also defines a matroid, and also depends on the characteristic of the fields. The algebraic characteristic set is defined in the similar way as the linear characteristic set.
The linear representations and characteristic sets are well studied. But the algebraic representations and …
Radio Number Of Hamming Graphs Of Diameter 3, Jason Devito, Amanda Niedzialomski, Jennifer Warren
Radio Number Of Hamming Graphs Of Diameter 3, Jason Devito, Amanda Niedzialomski, Jennifer Warren
Theory and Applications of Graphs
For $G$ a simple, connected graph, a vertex labeling $f:V(G)\to \Z_+$ is called a \emph{radio labeling of $G$} if it satisfies $f(u)f(v)\geq\diam(G)+1d(u,v)$ for all distinct vertices $u,v\in V(G)$. The \emph{radio number of $G$} is the minimal span over all radio labelings of $G$. If a bijective radio labeling onto $\{1,2,\dots,V(G)\}$ exists, $G$ is called a \emph{radio graceful} graph. We determine the radio number of all diameter 3 Hamming graphs and show that an infinite subset of them is radio graceful.
On The IntegerAntimagic Spectra Of NonHamiltonian Graphs, Wai Chee Shiu, Richard M. Low
On The IntegerAntimagic Spectra Of NonHamiltonian Graphs, Wai Chee Shiu, Richard M. Low
Theory and Applications of Graphs
Let $A$ be a nontrivial abelian group. A connected simple graph $G = (V, E)$ is $A$\textbf{antimagic} if there exists an edge labeling $f: E(G) \to A \setminus \{0\}$ such that the induced vertex labeling $f^+: V(G) \to A$, defined by $f^+(v) = \Sigma$ $\{f(u,v): (u, v) \in E(G) \}$, is a onetoone map. In this paper, we analyze the groupantimagic property for Cartesian products, hexagonal nets and theta graphs.
Restrained Reinforcement Number In Graphs, Kazhal Haghparast, Jafar Amjadi, Mustapha Chellali, Seyed Mahmoud Sheikholeslami
Restrained Reinforcement Number In Graphs, Kazhal Haghparast, Jafar Amjadi, Mustapha Chellali, Seyed Mahmoud Sheikholeslami
Theory and Applications of Graphs
A set $S$ of vertices is a restrained dominating set of a graph $G=(V,E)$ if every vertex in $V\setminus S$ has a neighbor in $S$ and a neighbor in $V\setminus S$. The minimum cardinality of a restrained dominating set is the restrained domination number $\gamma_{r}(G)$. In this paper we initiate the study of the restrained reinforcement number $r_{r}(G)$ of a graph $G$ defined as the cardinality of a smallest set of edges $F\subseteq E(\overline{G})$ for which $\gamma _{r}(G+F)
On PCompetition Graphs Of Loopless Hamiltonian Digraphs Without Symmetric Arcs And Graph Operations, Kuniharu Yokomura, Morimasa Tsuchiya
On PCompetition Graphs Of Loopless Hamiltonian Digraphs Without Symmetric Arcs And Graph Operations, Kuniharu Yokomura, Morimasa Tsuchiya
Theory and Applications of Graphs
For a digraph $D$, the $p$competition graph $C_{p}(D)$ of $D$ is the graph satisfying the following: $V(C_{p}(D))=V(D)$, for $x,y \in V(C_{p}(D))$, $xy \in E(C_{p}(D))$ if and only if there exist distinct $p$ vertices $v_{1},$ $v_{2},$ $...,$ $v_{p}$ $\in$ $V(D)$ such that $x \rightarrow v_{i}$, $y \rightarrow v_{i}$ $\in$ $A(D)$ for each $i=1,2,$ $...,$ $p$.
We show the $H_1 \cup H_2$ is a $p$competition graph of a loopless digraph without symmetric arcs for $p \geq 2$, where $H_1$ and $H_2$ are $p$competition graphs of loopless digraphs without symmetric arcs and $V(H_1) \cap V(H_2)$ $=$ $\{ \alpha \}$. For $p$competition graphs of …
Harmonious Labelings Via Cosets And Subcosets, Jared L. Painter, Holleigh C. Landers, Walker M. Mattox
Harmonious Labelings Via Cosets And Subcosets, Jared L. Painter, Holleigh C. Landers, Walker M. Mattox
Theory and Applications of Graphs
In [Abueida, A. and Roblee, K., More harmonious labelings of families of disjoint unions of an odd cycle and certain trees, J. Combin. Math. Combin. Comput., 115 (2020), 6168] it is shown that the disjoint union of an odd cycle and certain paths is harmonious, and that certain starlike trees are harmonious using properties of cosets for a particular subgroup of the integers modulo m, where m is the number of edges of the graph. We expand upon these results by first exploring the numerical properties when adding values from cosets and subcosets in the integers modulo m. We will …
Total Colouring Of New Classes Of Subcubic Graphs, Sethuraman G, Velankanni Anthonymuthu
Total Colouring Of New Classes Of Subcubic Graphs, Sethuraman G, Velankanni Anthonymuthu
Theory and Applications of Graphs
The total chromatic number of a graph $G$, denoted $\chi^{\prime\prime}(G)$, is the least number of colours needed to colour the vertices and the edges of $G$ such that no incident or adjacent elements (vertices or edges) receive the same colour. The popular Total Colouring Conjecture (TCC) posed by Behzad states that, for every simple graph $G$, $\chi^{\prime\prime}(G) \leq \Delta(G)+2$. In this paper, we prove that the total chromatic number for a family of subcubic graphs called cube connected paths and also for a class of subcubic graphs having the property that the vertices are covered by independent triangles are exactly …
On The Total Set Chromatic Number Of Graphs, Mark Anthony C. Tolentino, Gerone Russel J. Eugenio, MariJo P. Ruiz
On The Total Set Chromatic Number Of Graphs, Mark Anthony C. Tolentino, Gerone Russel J. Eugenio, MariJo P. Ruiz
Theory and Applications of Graphs
Given a vertex coloring c of a graph, the neighborhood color set of a vertex is defined to be the set of all of its neighbors’ colors. The coloring c is called a set coloring if any two adjacent vertices have different neighborhood color sets. The set chromatic number χ_{s}(G) of a graph G is the minimum number of colors required in a set coloring of G. In this work, we investigate a total analog of set colorings; that is, we study set colorings of the total graph of graphs. Given a graph G = (V, …
Geodesic Bipancyclicity Of The Cartesian Product Of Graphs, Amruta V. Shinde, Y.M. Borse
Geodesic Bipancyclicity Of The Cartesian Product Of Graphs, Amruta V. Shinde, Y.M. Borse
Theory and Applications of Graphs
A cycle containing a shortest path between two vertices $u$ and $v$ in a graph $G$ is called a $(u,v)$geodesic cycle. A connected graph $G$ is geodesic 2bipancyclic, if every pair of vertices $u,v$ of it is contained in a $(u,v)$geodesic cycle of length $l$ for each even integer $l$ satisfying $2d + 2\leq l \leq V(G),$ where $d$ is the distance between $u$ and $v.$ In this paper, we prove that the Cartesian product of two geodesic hamiltonian graphs is a geodesic 2bipancyclic graph. As a consequence, we show that for $n \geq 2$ every $n$dimensional torus is a …
OneFactorizations Of The Complete Graph $K_{P+1}$ Arising From Parabolas, György Kiss, Nicola Pace, Angelo Sonnino
OneFactorizations Of The Complete Graph $K_{P+1}$ Arising From Parabolas, György Kiss, Nicola Pace, Angelo Sonnino
Theory and Applications of Graphs
There are three types of affine regular polygons in AG(2, q): ellipse, hyperbola and parabola. The first two cases have been investigated in previous papers. In this note, a particular class of geometric onefactorizations of the complete graph K_{n} arising from parabolas is constructed and described in full detail. With the support of computer aided investigation, it is also conjectured that up to isomorphisms this is the only onefactorization where each onefactor is either represented by a line or a parabola.