Discrete Mathematics and Combinatorics | Open Access Articles

Approximation By The K^Lambda Means Of Fourier Series And Conjugate Series Of Functions In H_{Alpha,P}, Ben Landon, Holly Carley, R. N. Mohapatra

Publications and Research

No abstract provided.

Addendum For The Article Radio Graceful Labelling Of Graphs, Laxman Saha, Alamgir Rahaman Basunia

Theory & Applications of Graphs

Additional references listed for the article: Saha, Laxman and Basunia, Alamgir Rahaman (2020) "Radio Graceful Labelling of Graphs," Theory and Applications of Graphs: Vol. 7: Iss. 1, Article 7. DOI: 10.20429/tag.2020.070107

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Super Sudoku Squares, Dean Hoffman

Communications on Number Theory and Combinatorial Theory

We refer to a completed Sudoku puzzle as a Sudoku Square of order 3. We define a more restricted, but natural, extension --- a Super Sudoku Square of order n, and determine for which orders n one exists.

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Prime Supporters In College Students' Support Networks, David Chan, Hollee Mcginnis, Michael Broda, Haya Hamid, Jeremy Winslow, Quindel Jones, Joy Ma

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Algebraic And Combinatorial Approaches For Counting Cycles Arising In Population Biology, Brian Chau

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Dna Self-Assembly Design For Gear Graphs, Chiara Mattamira

Rose-Hulman Undergraduate Mathematics Journal

Application of graph theory to the well-known complementary properties of DNA strands has resulted in new insights about more efficient ways to form DNA nanostructures, which have been discovered as useful tools for drug delivery, biomolecular computing, and biosensors. The key concept underlying DNA nanotechnology is the formation of complete DNA complexes out of a given collection of branched junction molecules. These molecules can be modeled in the abstract as portions of graphs made up of vertices and half-edges, where complete edges are representations of double-stranded DNA pieces that have joined together. For efficiency, one aim is to minimize the …

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The Name Tag Problem, Christian Carley

Rose-Hulman Undergraduate Mathematics Journal

The Name Tag Problem is a thought experiment that, when formalized, serves as an introduction to the concept of an orthomorphism of $\Zn$. Orthomorphisms are a type of group permutation and their graphs are used to construct mutually orthogonal Latin squares, affine planes and other objects. This paper walks through the formalization of the Name Tag Problem and its linear solutions, which center around modular arithmetic. The characterization of which linear mappings give rise to these solutions developed in this paper can be used to calculate the exact number of linear orthomorphisms for any additive group Z/nZ, which is demonstrated …

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Investigating First Returns: The Effect Of Multicolored Vectors, Shakuan Frankson, Myka Terry

Rose-Hulman Undergraduate Mathematics Journal

By definition, a first return is the immediate moment that a path, using vectors in the Cartesian plane, touches the x-axis after leaving it previously from a given point; the initial point is often the origin. In this case, using certain diagonal and horizontal vectors while restricting the movements to the first quadrant will cause almost every first return to end at the point (2n,0), where 2n counts the equal number of up and down steps in a path. The exception will be explained further in the sections below. Using the first returns of Catalan, Schröder, and Motzkin numbers, which …

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On The Enumeration Of Shapes, May Cai, Nicholas Liao

Rose-Hulman Undergraduate Mathematics Journal

We define a shape as a union of finitely many line segments. Given an arrangement of lines on a plane, we count the number of shapes in the arrangement by examining the symmetries of the arrangement and applying Burnside's lemma. We further establish a generating function for the number of distinct line segments on a line with k distinguished points. We list all affine line arrangements of four and five line segments, together with the corresponding number of shapes on them.

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Iterated Line Graphs On Bi-Regular Graphs And Trees, Brenden Balch

Rose-Hulman Undergraduate Mathematics Journal

In 1965, van Rooij and Wilf considered sequences of line graphs, in which they grouped sequences of line graphs into four categories. We’ll add to their research by presenting results on sequences of line graphs for star graphs and bi-regular graphs. We will then investigate slight variations of star graphs.

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Legendre G-Array Pairs And The Theoretical Unification Of Several G-Array Families, K. T. Arasu, Dursun A. Bulutoglu, J. R. Hollon

Faculty Publications

We investigate how Legendre G-array pairs are related to several different perfect binary G-array families. In particular we study the relations between Legendre G-array pairs, Sidelnikov-Lempel-Cohn-Eastman ℤ_q−1-arrays, Yamada-Pott G-array pairs, Ding-Helleseth-Martinsen ℤ₂×ℤ^m_p-arrays, Yamada ℤ_(q−1)/2-arrays, Szekeres ℤ^m_p-array pairs, Paley ℤ^m_p-array pairs, and Baumert ℤ^m1_p1×ℤ^m2_p2-array pairs. Our work also solves one of the two open problems posed in Ding~[J. Combin. Des. 16 (2008), 164-171]. Moreover, we provide several computer search based existence and non-existence results regarding Legendre ℤ_n-array pairs. …

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Some Generalizations Of Classical Integer Sequences Arising In Combinatorial Representation Theory, Sasha Verona Malone

Masters Theses & Specialist Projects

There exists a natural correspondence between the bases for a given finite-dimensional representation of a complex semisimple Lie algebra and a certain collection of finite edge-colored ranked posets, laid out by Donnelly, et al. in, for instance, [Don03]. In this correspondence, the Serre relations on the Chevalley generators of the given Lie algebra are realized as conditions on coeﬀicients assigned to poset edges. These conditions are the so-called diamond, crossing, and structure relations (hereinafter DCS relations.) New representation constructions of Lie algebras may thus be obtained by utilizing edge-colored ranked posets. Of particular combinatorial interest are those representations whose corresponding …

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Quasilinearization Applied To Boundary Value Problems At Resonance For Riemann-Liouville Fractional Differential Equations, Paul W. Eloe, Jaganmohan Jonnalagadda

Mathematics Faculty Publications

The quasilinearization method is applied to a boundary value problem at resonance for a Riemann-Liouville fractional differential equation. Under suitable hypotheses, the method of upper and lower solutions is employed to establish uniqueness of solutions. A shift method, coupled with the method of upper and lower solutions, is applied to establish existence of solutions. The quasilinearization algorithm is then applied to obtain sequences of lower and upper solutions that converge monotonically and quadratically to the unique solution of the boundary value problem at resonance.

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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.

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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.

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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 …

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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 …

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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 …

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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 …

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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 C_n 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 …

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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 .

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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 …

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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,..., …

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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.

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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 …

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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 …

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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. …

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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.

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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.

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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 …

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Full-Text Articles in Discrete Mathematics and Combinatorics

Approximation By The K^Lambda Means Of Fourier Series And Conjugate Series Of Functions In H_{Alpha,P}, Ben Landon, Holly Carley, R. N. Mohapatra

Publications and Research

Addendum For The Article Radio Graceful Labelling Of Graphs, Laxman Saha, Alamgir Rahaman Basunia

Theory & Applications of Graphs

Super Sudoku Squares, Dean Hoffman

Communications on Number Theory and Combinatorial Theory

Prime Supporters In College Students' Support Networks, David Chan, Hollee Mcginnis, Michael Broda, Haya Hamid, Jeremy Winslow, Quindel Jones, Joy Ma

Annual Symposium on Biomathematics and Ecology Education and Research

Algebraic And Combinatorial Approaches For Counting Cycles Arising In Population Biology, Brian Chau

Annual Symposium on Biomathematics and Ecology Education and Research

Dna Self-Assembly Design For Gear Graphs, Chiara Mattamira

Rose-Hulman Undergraduate Mathematics Journal

The Name Tag Problem, Christian Carley

Rose-Hulman Undergraduate Mathematics Journal

Investigating First Returns: The Effect Of Multicolored Vectors, Shakuan Frankson, Myka Terry

Rose-Hulman Undergraduate Mathematics Journal

On The Enumeration Of Shapes, May Cai, Nicholas Liao

Rose-Hulman Undergraduate Mathematics Journal

Iterated Line Graphs On Bi-Regular Graphs And Trees, Brenden Balch

Rose-Hulman Undergraduate Mathematics Journal

Legendre G-Array Pairs And The Theoretical Unification Of Several G-Array Families, K. T. Arasu, Dursun A. Bulutoglu, J. R. Hollon

Faculty Publications

Some Generalizations Of Classical Integer Sequences Arising In Combinatorial Representation Theory, Sasha Verona Malone

Masters Theses & Specialist Projects

Quasilinearization Applied To Boundary Value Problems At Resonance For Riemann-Liouville Fractional Differential Equations, Paul W. Eloe, Jaganmohan Jonnalagadda

Mathematics Faculty Publications

Isomorphism Of Trees And Isometry Of Ultrametric Spaces, Oleksiy Dovgoshey

Theory & Applications of Graphs

Arithmetical Structures On Paths With A Doubled Edge, Darren B. Glass, Joshua R. Wagner

Math Faculty Publications

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

Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, Bhavana Panchumarthi, Monroe Ame Stephenson

altREU Projects

Decomposition Of Certain Complete Graphs And Complete Multipartite Graphs Into Almost-Bipartite Graphs And Bipartite Graphs, G. Sethuraman, M. Sujasree

Theory & Applications of Graphs

Some Results On Seymour’S Second-Neighborhood Conjecture And On Decompositions Of Graphs, Farid Bouya

LSU Doctoral Dissertations

Laplacian Spectral Properties Of Signed Circular Caterpillars, Maurizio Brunetti

Theory & Applications of Graphs

Infinite Sets Of Solutions And Almost Solutions Of The Equation N∙M = Reversal(N∙M) Ii, Viorel Nitica, Cem Ekinci

Mathematics Faculty Publications

The Burning Number Of Directed Graphs: Bounds And Computational Complexity, Remie Janssen

Theory & Applications of Graphs

Logarithmic Mean Labeling Of Some Ladder Related Graphs, A. Durai Baskar

Applications and Applied Mathematics: An International Journal (AAM)

Twin Edge Coloring Of Total Graph And Graphs With Twin Chromatic Index 𝚫+𝟐, S. Anantharaman

Applications and Applied Mathematics: An International Journal (AAM)

Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan

Electronic Theses, Projects, and Dissertations

Pemahaman Murid Tingkatan Lima Tentang Konsep Dalam Topik Janjang Aritmetik, Edwar Siti Zaharah

Student Works (2020-2029)

Radio Graceful Labelling Of Graphs, Laxman Saha, Alamgir Rahaman Basunia

Theory & Applications of Graphs

Domination Number Of Annulus Triangulations, Toshiki Abe, Junki Higa, Shin-Ichi Tokunaga

Theory & Applications of Graphs

Lattice Paths In Diagonals And Dimensions, Freya Bennett

Honors Theses

Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges

LSU Doctoral Dissertations