Mathematical Models: The Lanchester Equations And The Zombie Apocalypse,
2019
University of Lynchburg
Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Undergraduate Theses and Capstone Projects
This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic models. …
Series-Parallel Operations With Alpha-Graphs,
2019
Valencia College
Series-Parallel Operations With Alpha-Graphs, Christian Barrientos, Sarah Minion
Theory & Applications of Graphs
Among difference vertex labelings of graphs, α-labelings are the most restrictive one. A graph is an α-graph if it admits an α-labeling. In this work, we study a new alternative to construct α-graphs using, the well-known, series-parallel operations on smaller α-graphs. As an application of the series operation, we show that all members of a subfamily of all trees with maximum degree 4, obtained using vertex amalgamation of copies of the path Ρ11}, are α-graphs. We also show that the one-point union of up to four copies of Κn,n is an …
Fractional Matching Preclusion For Butterfly Derived Networks,
2019
Qinghai University
Fractional Matching Preclusion For Butterfly Derived Networks, Xia Wang, Tianlong Ma, Chengfu Ye, Yuzhi Xiao, Fang Wang
Theory & Applications of Graphs
The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu [18] recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of G, denoted by fmp(G), is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of G, denoted by fsmp(G), is the minimum number of vertices and edges whose deletion …
Blackjack: The Math Behind The Cards,
2019
Louisiana Tech University
Blackjack: The Math Behind The Cards, Hanna Blanchard
Mathematics Senior Capstone Papers
In this paper the reader will learn about the math behind the cards in the game of Blackjack. Blackjack or “21” has been played around the world with various rules and regulations in both professional and informal environments. The ultimate objective of the game is to receive a total card value of 21, or as close to 21 as possible without exceeding it, from the cards in a player’s hand in order to beat the dealer’s total. The goal of this project is to calculate the probabilities of various hands to determine the best strategies to win 21. The probabilities …
Greatest Common Divisor: Algorithm And Proof,
2019
University of St. Thomas - Houston
Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg
Number Theory
No abstract provided.
Congruence Relations Mod 2 For (2 X 4^T + 1)-Colored Partitions,
2019
University of South Carolina
Congruence Relations Mod 2 For (2 X 4^T + 1)-Colored Partitions, Nicholas Torello
Senior Theses
Let p_r(n) denote the difference between the number of r-colored partitions of n into an even number of distinct parts and into an odd number of distinct parts. Inspired by proofs involving modular forms of the Hirschhorn-Sellers Conjecture, we prove a similar congruence for p_r(n). Using the Jacobi Triple Product identity, we discover a much stricter congruence for p_3(n).
The Knill Graph Dimension From Clique Cover,
2019
Pepperdine
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.
Triangle Packing On Tripartite Graphs Is Hard,
2019
University of Kansas
Triangle Packing On Tripartite Graphs Is Hard, Peter A. Bradshaw
Rose-Hulman Undergraduate Mathematics Journal
The problem of finding a maximum matching on a bipartite graph is well-understood and can be solved using the augmenting path algorithm. However, the similar problem of finding a large set of vertex-disjoint triangles on tripartite graphs has not received much attention. In this paper, we define a set of vertex-disjoint triangles as a “tratching.” The problem of finding a tratching that covers all vertices of a tripartite graph can be shown to be NP-complete using a reduction from the three-dimensional matching problem. In this paper, however, we introduce a new construction that allows us to emulate Boolean circuits using …
Graphs, Random Walks, And The Tower Of Hanoi,
2019
Baldwin Wallace University, Berea
Graphs, Random Walks, And The Tower Of Hanoi, Stephanie Egler
Rose-Hulman Undergraduate Mathematics Journal
The Tower of Hanoi puzzle with its disks and poles is familiar to students in mathematics and computing. Typically used as a classroom example of the important phenomenon of recursion, the puzzle has also been intensively studied its own right, using graph theory, probability, and other tools. The subject of this paper is “Hanoi graphs”, that is, graphs that portray all the possible arrangements of the puzzle, together with all the possible moves from one arrangement to another. These graphs are not only fascinating in their own right, but they shed considerable light on the nature of the puzzle itself. …
Asymptotically Optimal Bounds For (𝑡,2) Broadcast Domination On Finite Grids,
2019
Williams College
Asymptotically Optimal Bounds For (𝑡,2) Broadcast Domination On Finite Grids, Timothy W. Randolph
Rose-Hulman Undergraduate Mathematics Journal
Let G = (V,E) be a graph and t,r be positive integers. The signal that a tower vertex T of signal strength t supplies to a vertex v is defined as sig(T, v) = max(t − dist(T,v),0), where dist(T,v) denotes the distance between the vertices v and T. In 2015 Blessing, Insko, Johnson, and Mauretour defined a (t, r) broadcast dominating set, or simply a (t, r) broadcast, on G as a set T ⊆ V such that the sum of all signal received at each vertex v ∈ V from the set of towers T …
A Generalized Newton-Girard Identity,
2019
University of Maryland, College Park
A Generalized Newton-Girard Identity, Tanay Wakhare
Rose-Hulman Undergraduate Mathematics Journal
We present a generalization of the Newton-Girard identities, along with some applications. As an addendum, we collect many evaluations of symmetric polynomials to which these identities apply.
The Knill Graph Dimension From The Minimum Clique Cover,
2019
San Jose State University
The Knill Graph Dimension From The Minimum Clique Cover, Kassahun Betre, Evatt Salinger
Faculty Publications
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+dimG1+dimG2. 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 N will have dimension N−1. We finish by finding lower and upper bounds on the Knill dimension of a graph in terms of its clique number.
Two-Pebbling And Odd-Two-Pebbling Are Not Equivalent,
2019
Hope College
Two-Pebbling And Odd-Two-Pebbling Are Not Equivalent, Charles A. Cusack, Airat Bekmetjev, Mark Powers
Faculty Publications
Let G be a connected graph. A configuration of pebbles assigns a nonnegative integer number of pebbles to each vertex of G. A move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. A configuration is solvable if any vertex can get at least one pebble through a sequence of moves. The pebbling number of G, denoted π(G), is the smallest integer such that any configuration of π(G) pebbles on G is solvable. A graph has the two-pebbling property if after placing more than 2π(G) -- q pebbles on G …
Singular Ramsey And Turán Numbers,
2019
University of Haifa-Oranim
Singular Ramsey And Turán Numbers, Yair Caro, Zsolt Tuza
Theory & Applications of Graphs
We say that a subgraph F of a graph G is singular if the degrees dG(v) are all equal or all distinct for the vertices v ∈ V (F). The singular Ramsey number Rs(F) is the smallest positive integer n such that, for every m at least n, in every edge 2-coloring of Km, at least one of the color classes contains F as a singular subgraph. In a similar flavor, the singular Turán number Ts(n,F) is defined as the maximum number of edges in a graph of order n, …
Analysis Of Feast Spectral Approximations Using The Dpg Discretization,
2019
Portland State University
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Quanah Parker
Mathematics and Statistics Faculty Publications and Presentations
A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of …
Computing Homology Of Hypergraphs,
2019
Illinois State University
Computing Homology Of Hypergraphs, Jackson Earl
STAR Program Research Presentations
In the modern age of data science, the necessity for efficient and insightful analytical tools that enable us to interpret large data structures inherently presents itself. With the increasing utility of metrics offered by the mathematics of hypergraph theory and algebraic topology, we are able to explore multi-way relational datasets and actively develop such tools. Throughout this research endeavor, one of the primary goals has been to contribute to the development of computational algorithms pertaining to the homology of hypergraphs. More specifically, coding in python to compute the homology groups of a given hypergraph, as well as their Betti numbers …
Bounding The Number Of Compatible Simplices In Higher Dimensional Tournaments,
2019
University of Kentucky
Bounding The Number Of Compatible Simplices In Higher Dimensional Tournaments, Karthik Chandrasekhar
Theses and Dissertations--Mathematics
A tournament graph G is a vertex set V of size n, together with a directed edge set E ⊂ V × V such that (i, j) ∈ E if and only if (j, i) ∉ E for all distinct i, j ∈ V and (i, i) ∉ E for all i ∈ V. We explore the following generalization: For a fixed k we orient every k-subset of V by assigning it an orientation. That is, every facet of the (k − 1)-skeleton of the ( …
Squared Distance Matrix Of A Weighted Tree,
2019
Indian Statistical Institute (Delhi Centre)
Squared Distance Matrix Of A Weighted Tree, Ravindra B. Bapat
Journal Articles
Let T be a tree with vertex set f1;: :: ; ng such that each edge is assigned a nonzero weight. The squared distance matrix of T; denoted by is the n n matrix with (i; j)-element d(i; j)2; where d(i; j) is the sum of the weights of the edges on the (ij)-path. We obtain a formula for the determinant of A formula for 1 is also obtained, under certain conditions. The results generalize known formulas for the unweighted case.
On Monochromatic Sets With Nondecreasing Diameter,
2019
Marshall University
On Monochromatic Sets With Nondecreasing Diameter, Adam O’Neal
Theses, Dissertations and Capstones
Our problem comes from the field of combinatorics known as Ramsey theory. Ramsey theory, in a general sense, is about identifying the threshold for which a family of objects, associated with a particular parameter, goes from never or sometimes satisfying a certain property to always satisfying that property. Research in Ramsey theory has applications in design theory and coding theory. For integers m, r, and t, we say that a set of n integers colored with r colors is (m, r, t)-permissible if there exist t monochromatic subsets B1, B2, . . . , Bt …
On The Existence Of Partitioned Incomplete Latin Squares With Five Parts,
2019
Marshall University
On The Existence Of Partitioned Incomplete Latin Squares With Five Parts, Jaromy Kuhl, Donald Mcginn, Michael W. Schroeder
Mathematics Faculty Research
Let a, b, c, d, e be positive integers such that a ≤ b ≤ c ≤ d ≤ e. Heinrich showed the existence of a partitioned incomplete Latin square (PILS) of type (a, b, c) and (a, b, c, d) if and only if a = b = c and 2a ≥ d. For PILS of type (a,b,c,d,e), it is necessary that a + b + c ≥ e, but not sufficient, and no characterization is currently known. In this talk we provide an additional …
