Invariant Sum Defined In Terms Of Complex Multivariate Polynomial Given Degree,
2019
Illinois Mathematics and Science Academy
Invariant Sum Defined In Terms Of Complex Multivariate Polynomial Given Degree, Matthew Niemiro '20
Exemplary Student Work
We use a generalized version of arithmetic progressions to obtain a non- trivial everywhere-zero sum in terms of a complex univariate polynomial and its degree. We then remark on its generalization to multivariate polynomials.
Some Results And Examples On Vertex Equitable Labeling,
2019
The British University in Egypt
Some Results And Examples On Vertex Equitable Labeling, Mohamed Saied Aboshady, Reda Amin Elbarkoki, Eliwa Mohamed Roshdy, Mohamed Abdel Azim Seoud
Basic Science Engineering
In this paper we present a survey for all graphs with order at most 6 whether they are vertex equitable or not and we get an upper bound for the number of edges of any graph with π vertices to be a vertex equitable graph. Also, we establish vertex equitable labeling for the π-chain of the complete bipartite graph πΎ2,π and for the graph ππ Γ ππ.
Adjacent Vertex-Distinguishing Proper Edge-Coloring Of Strong Product Of Graphs,
2019
Annamalai University
Adjacent Vertex-Distinguishing Proper Edge-Coloring Of Strong Product Of Graphs, S. Anantharaman
Applications and Applied Mathematics: An International Journal (AAM)
Let G be a finite, simple, undirected and connected graph. The adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for a proper edge-coloring of G, in which no two adjacent vertices are incident to edges colored with the same set of colors. The minimum number of colors required for an adjacent vertex-distinguishing proper edgecoloring of G is called the adjacent vertex-distinguishing proper edge-chromatic index. In this paper, I compute adjacent vertex-distinguishing proper edge-chromatic index of strong product of graphs.
The Weak Hyperedge Tenacity Of The Hypercycles,
2019
University of Qom
The Weak Hyperedge Tenacity Of The Hypercycles, G. H. Shirdel, B. Vaez-Zadeh
Applications and Applied Mathematics: An International Journal (AAM)
Graphs play an important role in our daily life. For example, the urban transport network can be represented by a graph, as the intersections are the vertices and the streets are the edges of the graph. Suppose that some edges of the graph are removed, the question arises how damaged the graph is. There are some criteria for measuring the vulnerability of graph; the tenacity is the best criteria for measuring it. Since the hypergraph generalize the standard graph by defining any edge between multiple vertices instead of only two vertices, the above question is about the hypergraph. When a β¦
Rank Reduction Of String C-Group Representations,
2019
Bucknell University
Rank Reduction Of String C-Group Representations, Peter A. Brooksbank, Dimitri Leemans
Faculty Journal Articles
We show that a rank reduction technique for string C-group representations first used in [Adv. Math. 228 (2018), pp. 3207β3222] for the symmetric groups generalizes to arbitrary settings. The technique permits us, among other things, to prove that orthogonal groups defined on d-dimensional modules over fields of even order greater than 2 possess string C-group representations of all ranks. The broad applicability of the rank reduction technique provides fresh impetus to construct, for suitable families of groups, string C-groups of highest possible rank. It also suggests that the alternating group Alt(11)βthe only known group having βrank gapsββis perhaps more unusual β¦
Conditional Strong Matching Preclusion Of The Alternating Group Graph,
2019
American University of Kuwait
Conditional Strong Matching Preclusion Of The Alternating Group Graph, Mohamad Abdallah, Eddie Cheng
Theory & Applications of Graphs
The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. Park and Ihm introduced the problem of strong matching preclusion under the condition that no isolated vertex is created as a result of faults. In this paper, we find the conditional strong matching preclusion number for the n-dimensional alternating group graph AGn.
Repeat Length Of Patterns On Weaving Products,
2019
Rose-Hulman Institute of Technology
Repeat Length Of Patterns On Weaving Products, Zhuochen Liu
Mathematical Sciences Technical Reports (MSTR)
Interlacing strands have been used to create artistic weaving patterns. Repeated patterns form aesthetically pleasing products. This research is a mathematical modeling of weaving products in the real world by using Cellular Automata. The research is conducted by observing the evolution of the model to better understand products in the real world. Specifically, this research focuses on the repeat length of a weaving pattern given the rule of generating it and the configuration of the starting row. Previous studies have shown the range of the repeat length in specific situations. This paper will generalize the precise repeat length in one β¦
Forcibly-Biconnected Graphical Degree Sequences: Decision Algorithms And Enumerative Results,
2019
Georgia Southern University
Forcibly-Biconnected Graphical Degree Sequences: Decision Algorithms And Enumerative Results, Kai Wang
Theory & Applications of Graphs
We present an algorithm to test whether a given graphical degree sequence is forcibly biconnected. The worst case time complexity of the algorithm is shown to be exponential but it is still much better than the previous basic algorithm for this problem. We show through experimental evaluations that the algorithm is efficient on average. We also adapt the classic algorithm of Ruskey et al. and that of Barnes and Savage to obtain some enumerative results about forcibly biconnected graphical degree sequences of given length n and forcibly biconnected graphical partitions of given even integer n. Based on these enumerative β¦
Laplacian Spectral Characterization Of Signed Sun Graphs,
2019
Shiraz University
Laplacian Spectral Characterization Of Signed Sun Graphs, Fatemeh Motialah, Mohammad Hassan Shirdareh Haghighi
Theory & Applications of Graphs
A sun SGn is a graph of order 2n consisting of a cycle Cn, n β₯ 3, to each vertex of it a pendant edge is attached. In this paper, we prove that unbalanced signed sun graphs are determined by their Laplacian spectra. Also we show that a balanced signed sun graph is determined by its Laplacian spectrum if and only if n is odd.
Sdrap: An Annotation Pipeline For Highly Scrambled Genomes,
2019
Illinois State University
Sdrap: An Annotation Pipeline For Highly Scrambled Genomes, Jasper Braun
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Models For Describing Molecular Self-Assembly,
2019
University of South Florida
Mathematical Models For Describing Molecular Self-Assembly, Margherita Maria Ferrari
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Loop Homology Of Bi-Secondary Structures,
2019
Illinois State University
Loop Homology Of Bi-Secondary Structures, Andrei Bura
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Design Of Experiments For Unique Wiring Diagram Identification,
2019
California Polytechnic State University, San Luis Obispo
Design Of Experiments For Unique Wiring Diagram Identification, Elena Dimitrova
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
On An Enhancement Of Rna Probing Data Using Information Theory,
2019
University of Virginia
On An Enhancement Of Rna Probing Data Using Information Theory, Thomas J.X. Li, Christian M. Reidys
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Research For Educators: Modeling Graph Theory For Nontraditional Math Researchers,
2019
Illinois State University
Research For Educators: Modeling Graph Theory For Nontraditional Math Researchers, Erwin Cornelius
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Controllability And Observability Of Linear Nabla Discrete Fractional Systems,
2019
Western Kentucky University
Controllability And Observability Of Linear Nabla Discrete Fractional Systems, Tilekbek Zhoroev
Masters Theses & Specialist Projects
The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we β¦
Fractional Strong Matching Preclusion For Two Variants Of Hypercubes,
2019
School of Computer, Qinghai Normal University
Fractional Strong Matching Preclusion For Two Variants Of Hypercubes, Huifen Ge, Tianlong Ma, Miaolin Wu, Yuzhi Xiao
Theory & Applications of Graphs
Let F be a subset of edges and vertices of a graph G. If G-F has no fractional perfect matching, then F is a fractional strong matching preclusion set of G. The fractional strong matching preclusion number is the cardinality of a minimum fractional strong matching preclusion set. In this paper, we mainly study the fractional strong matching preclusion problem for two variants of hypercubes, the multiply twisted cube and the locally twisted cube, which are two of the most popular interconnection networks. In addition, we classify all the optimal fractional strong matching preclusion set of each.
Colored Complete Hypergraphs Containing No Rainbow Berge Triangles,
2019
UPS of America, Inc.
Colored Complete Hypergraphs Containing No Rainbow Berge Triangles, Colton Magnant
Theory & Applications of Graphs
The study of graph Ramsey numbers within restricted colorings, in particular forbidding a rainbow triangle, has recently been blossoming under the name Gallai-Ramsey numbers. In this work, we extend the main structural tool from rainbow triangle free colorings of complete graphs to rainbow Berge triangle free colorings of hypergraphs. In doing so, some other concepts and results are also translated from graphs to hypergraphs.
Roman Domination Cover Rubbling,
2019
East Tennessee State University
Roman Domination Cover Rubbling, Nicholas Carney
Electronic Theses and Dissertations
In this thesis, we introduce Roman domination cover rubbling as an extension of domination cover rubbling. We define a parameter on a graph $G$ called the \textit{Roman domination cover rubbling number}, denoted $\rho_{R}(G)$, as the smallest number of pebbles, so that from any initial configuration of those pebbles on $G$, it is possible to obtain a configuration which is Roman dominating after some sequence of pebbling and rubbling moves. We begin by characterizing graphs $G$ having small $\rho_{R}(G)$ value. Among other things, we also obtain the Roman domination cover rubbling number for paths and give an upper bound for the β¦
Choose Your Own Adventure: An Analysis Of Interactive Gamebooks Using Graph Theory,
2019
Southwestern University
Choose Your Own Adventure: An Analysis Of Interactive Gamebooks Using Graph Theory, D'Andre Adams, Daniela Beckelhymer, Alison Marr
Journal of Humanistic Mathematics
"BEWARE and WARNING! This book is different from other books. You and YOU ALONE are in charge of what happens in this story." This is the captivating introduction to every book in the interactive novel series, Choose Your Own Adventure (CYOA). Our project uses the mathematical field of graph theory to analyze forty books from the CYOA book series for ages 9-12. We first began by drawing the digraphs of each book. Then we analyzed these digraphs by collecting structural data such as longest path length (i.e. longest story length) and number of vertices with outdegree zero (i.e. number β¦
