Isomorphism Of Trees And Isometry Of Ultrametric Spaces,
2020
Institute of Applied Mathematics and Mechanics of NASU of Ukraine
Isomorphism Of Trees And Isometry Of Ultrametric Spaces, Oleksiy Dovgoshey
Theory & Applications of Graphs
We study the conditions under which the isometry of spaces with metrics generated by weights given on the edges of finite trees is equivalent to the isomorphism of these trees. Similar questions are studied for ultrametric spaces generated by labelings given on the vertices of trees. The obtained results generalized some facts previously known for phylogenetic trees and for Gurvich---Vyalyi monotone trees.
Arithmetical Structures On Paths With A Doubled Edge,
2020
Gettysburg College
Arithmetical Structures On Paths With A Doubled Edge, Darren B. Glass, Joshua R. Wagner
Math Faculty Publications
An arithmetical structure on a graph is given by a labeling of the vertices that satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical structures for graphs in these families.
A Theory Of Preimage Complexity: Data-Structures, Complexity Measures And Applications To Endofunctions And Associated Digraphs,
2020
University of New Orleans
A Theory Of Preimage Complexity: Data-Structures, Complexity Measures And Applications To Endofunctions And Associated Digraphs, Bradford M. Fournier-Eaton
LSU New Orleans Theses and Dissertations
This dissertation develops a new theory of finite function complexity. This novel approach is based on the structure of preimage sets generated under repeat application of the inverse. We encode this information in our primary data-structure, an square matrix called the sigma matrix. This matrix allows us to easily encode information about the functional digraph and cycle structure of the associated endofunction. Additionally, the sigma matrix is of interest in its own right. The columns of sigma matrices are integer partitions of the domain size n, the size of the domain is always an eigenvalue of the sigma matrix, and …
Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model,
2020
Reed College
Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, Bhavana Panchumarthi, Monroe Ame Stephenson
altREU Projects
A Distributed Denial of Service (DDoS) is a cyber attack, which is capable of triggering a cascading failure in the victim network. While DDoS attacks come in different forms, their general goal is to make a network's service unavailable to its users. A common, but risky, countermeasure is to blackhole or null route the source, or the attacked destination. When a server becomes a blackhole, or referred to as the sink in the paper, the data that is assigned to it "disappears" or gets deleted. Our research shows how mathematical modeling can propose an alternative blackholing strategy that could improve …
Decomposition Of Certain Complete Graphs And Complete Multipartite Graphs Into Almost-Bipartite Graphs And Bipartite Graphs,
2020
Anna University, Chennai
Decomposition Of Certain Complete Graphs And Complete Multipartite Graphs Into Almost-Bipartite Graphs And Bipartite Graphs, G. Sethuraman, M. Sujasree
Theory & Applications of Graphs
In his classical paper [14], Rosa introduced a hierarchical series of labelings called ρ, σ, β and α labeling as a tool to settle Ringel’s Conjecture which states that if T is any tree with m edges then the complete graph K2m+1 can be decomposed into 2m + 1 copies of T . Inspired by the result of Rosa [14] many researchers significantly contributed to the theory of graph decomposition using graph labeling. In this direction, in 2004, Blinco et al. [6] introduced γ-labeling as a stronger version of ρ-labeling. A function g defined on the vertex set …
Some Results On Seymour’S Second-Neighborhood Conjecture And On Decompositions Of Graphs,
2020
Louisiana State University
Some Results On Seymour’S Second-Neighborhood Conjecture And On Decompositions Of Graphs, Farid Bouya
LSU Doctoral Dissertations
This dissertation consists of two parts. In the first part, I examine Seymour’s Second-Neighborhood Conjecture, which states that every orientation of every simple graph has at least one vertex v such that the number of vertices of out-distance 2 from v is at least as large as the number of vertices of out-distance 1 from it. I present alternative statements of this conjecture using the language of linear algebra, the last one being completely in terms of the inverse of some matrix. In the second part of this dissertation, comprising of Chapters 2 and 3, I examine two conjectures on …
Laplacian Spectral Properties Of Signed Circular Caterpillars,
2020
University of Naples `Federico II' Italy
Laplacian Spectral Properties Of Signed Circular Caterpillars, Maurizio Brunetti
Theory & Applications of Graphs
A circular caterpillar of girth n is a graph such that the removal of all pendant vertices yields a cycle Cn of order n. A signed graph is a pair Γ =(G,σ), where G is a simple graph and σ: E(G) →{+1, -1} is the sign function defined on the set E(G) of edges of G. The signed graph Γ is said to be balanced if the number of negatively signed edges in each cycle is even, and it is said to be unbalanced otherwise. We determine some bounds for the first n Laplacian eigenvalues …
Infinite Sets Of Solutions And Almost Solutions Of The Equation N∙M = Reversal(N∙M) Ii,
2020
West Chester University of Pennsylvania
Infinite Sets Of Solutions And Almost Solutions Of The Equation N∙M = Reversal(N∙M) Ii, Viorel Nitica, Cem Ekinci
Mathematics Faculty Publications
Motivated by their intrinsic interest and by applications to the study of numeric palindromes and other sequences of integers, we discover a method for producing infinite sets of solutions and almost solutions of the equation N M reversal N M ⋅= ⋅ ( ) , our results are valid in a general numeration base b > 2 .
The Burning Number Of Directed Graphs: Bounds And Computational Complexity,
2020
Delft University of Technology
The Burning Number Of Directed Graphs: Bounds And Computational Complexity, Remie Janssen
Theory & Applications of Graphs
The burning number of a graph was recently introduced by Bonato et al. Although they mention that the burning number generalizes naturally to directed graphs, no further research on this has been done. Here, we introduce graph burning for directed graphs, and we study bounds for the corresponding burning number and the hardness of finding this number. We derive sharp bounds from simple algorithms and examples. The hardness question yields more surprising results: finding the burning number of a directed tree with one indegree-0 node is NP-hard, but FPT; however, it is W[2]-complete for DAGs. Finally, we give a fixed-parameter …
Dna Complexes Of One Bond-Edge Type,
2020
California State University - San Bernardino
Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan
Electronic Theses, Projects, and Dissertations
DNA self-assembly is an important tool used in the building of nanostructures and targeted virotherapies. We use tools from graph theory and number theory to encode the biological process of DNA self-assembly. The principal component of this process is to examine collections of branched junction molecules, called pots, and study the types of structures that such pots can realize. In this thesis, we restrict our attention to pots which contain identical cohesive-ends, or a single bond-edge type, and we demonstrate the types and sizes of structures that can be built based on a single characteristic of the pot that is …
Logarithmic Mean Labeling Of Some Ladder Related Graphs,
2020
CSI Jayaraj Annapackiam College
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,..., …
Twin Edge Coloring Of Total Graph And Graphs With Twin Chromatic Index 𝚫+𝟐,
2020
Annamalai University
Twin Edge Coloring Of Total Graph And Graphs With Twin Chromatic Index 𝚫+𝟐, S. Anantharaman
Applications and Applied Mathematics: An International Journal (AAM)
A twin edge coloring of a graph G is meant a proper edge coloring of G whose colors come from the integers modulo k that induce a proper vertex coloring in which the color of a vertex is the sum of the colors of its incident edges. The minimum k for which G has a twin edge coloring is the twin chromatic index of G. In this paper, I compute twin chromatic index of total graph of path and cycle also construct some special graphs with twin chromatic index is maximum degree plus two.
Pemahaman Murid Tingkatan Lima Tentang Konsep Dalam Topik Janjang Aritmetik,
2020
Universiti Malaya
Pemahaman Murid Tingkatan Lima Tentang Konsep Dalam Topik Janjang Aritmetik, Edwar Siti Zaharah
Student Works (2020-2029)
Janjang Aritmetik merupakan tajuk yang sangat penting bagi murid Tingkatan Lima yang mengambil matapelajaran elektif Matematik Tambahan. Tujuan kajian ini dijalankan adalah untuk mengetahui pemahaman murid Tingkatan Lima tentang konsep dalam topik janjang aritmetik. Seramai empat orang murid Tingkatan Lima dipilih dalam kajian ini menggunakan kaedah persampelan bertujuan. Mereka belajar di sebuah sekolah menengah di Selangor. Kajian ini dijalankan berlandaskan teori konstruktivisme radikal. Kajian kes digunakan bagi mengumpulkan data melalui empat sesi temu bual klinikal yang melibatkan gambaran mental, perwakilan, makna dan penyelesaian masalah. Setiap sesi temu duga dirakam dengan alat perakam video. Data kajian dalam bentuk jawapan bertulis dan …
Radio Graceful Labelling Of Graphs,
2020
Balurghat College
Radio Graceful Labelling Of Graphs, Laxman Saha, Alamgir Rahaman Basunia
Theory & Applications of Graphs
Radio labelling problem of graphs have their roots in communication problem known as Channel Assignment Problem. For a simple connected graph G=(V(G), E(G)), a radio labeling is a mapping f : V(G) →{0,1,2,…} such that |f(u)-f(v)|≥ diam(G)+1-d(u,v) for each pair of distinct vertices u,v ∈ V(G), where diam(G) is the diameter of G and d(u,v) is the distance between u and v. A radio labeling f of a graph G is a radio graceful labeling of G if f(V(G)) = {0,1,… |V(G)|-1}. A graph for which a radio graceful labeling exists is called radio graceful. …
Domination Number Of Annulus Triangulations,
2020
Yokohama National University
Domination Number Of Annulus Triangulations, Toshiki Abe, Junki Higa, Shin-Ichi Tokunaga
Theory & Applications of Graphs
An annulus triangulation G is a 2-connected plane graph with two disjoint faces f1 and f2 such that every face other than f1 and f2 are triangular, and that every vertex of G is contained in the boundary cycle of f1 or f2. In this paper, we prove that every annulus triangulation G with t vertices of degree 2 has a dominating set with cardinality at most ⌊ \frac{|V(G)|+t+1}{4} ⌋ if G is not isomorphic to the octahedron. In particular, this bound is best possible.
Lattice Paths In Diagonals And Dimensions,
2020
Coastal Carolina University
Lattice Paths In Diagonals And Dimensions, Freya Bennett
Honors Theses
The Lattice Paths of Combinatorics have been used in many applications, normally under the guise of a different name, due to its versatility in surface variety and specificity of answer. The Lattice Path’s of game development, in finding paths around barriers in mazes, is called Path Finder with the A∗ algorithms as its method of solving.
Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences,
2020
Louisiana State University and Agricultural and Mechanical College
Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges
LSU Doctoral Dissertations
Our main results are asymptotic zero-one laws satisfied by the diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane; the upper boundary is called the shape. For various types of unimodal sequences, we show that, as the number of squares tends to infinity, 100% of shapes are near a certain curve---that is, there is a single limit shape. Similar phenomena have been well-studied for integer partitions, but several technical difficulties arise in the extension of such asymptotic statistical laws to unimodal sequences. We develop a widely applicable method for obtaining these limit …
The Game Of Life On The Hyperbolic Plane,
2020
Rose-Hulman Institute of Technology
The Game Of Life On The Hyperbolic Plane, Yuncong Gu
Mathematical Sciences Technical Reports (MSTR)
In this paper, we work on the Game of Life on the hyperbolic plane. We are interested in different tessellations on the hyperbolic plane and different Game of Life rules. First, we show the exponential growth of polygons on the pentagon tessellation. Moreover, we find that the Group of 3 can keep the boundary of a set not getting smaller. We generalize the existence of still lifes by computer simulations. Also, we will prove some propositions of still lifes and cycles. There exists a still life under rules B1, B2, and S3.
The Game Of Cops And Robbers On Planar Graphs,
2020
Missouri State University
The Game Of Cops And Robbers On Planar Graphs, Jordon S. Daugherty
Graduate Theses/Dissertations
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 …
Target Control Of Networked Systems,
2020
University of New Mexico
Target Control Of Networked Systems, Isaac S. Klickstein
Mechanical Engineering ETDs
The control of complex networks is an emerging field yet it has already garnered interest from across the scientific disciplines, from robotics to sociology. It has quickly been noticed that many of the classical techniques from controls engineering, while applicable, are not as illuminating as they were for single systems of relatively small dimension. Instead, properties borrowed from graph theory provide equivalent but more practical conditions to guarantee controllability, reachability, observability, and other typical properties of interest to the controls engineer when dealing with large networked systems. This manuscript covers three topics investigated in detail by the author: (i) the …
