Open Access. Powered by Scholars. Published by Universities.®

Discrete Mathematics and Combinatorics Commons

Open Access. Powered by Scholars. Published by Universities.®

510 Full-Text Articles 605 Authors 50244 Downloads 63 Institutions

All Articles in Discrete Mathematics and Combinatorics

Faceted Search

510 full-text articles. Page 1 of 16.

Planar Graphs, Biplanar Graphs And Graph Thickness, Sean M. Hearon 2016 California State University - San Bernardino

Planar Graphs, Biplanar Graphs And Graph Thickness, Sean M. Hearon

Electronic Theses, Projects, and Dissertations

A graph is planar if it can be drawn on a piece of paper such that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph and the blue edges induce a planar subgraph. In this thesis, we determine the smallest complete and complete bipartite graphs that are not biplanar.


Potentially Nilpotent Tridiagonal Sign Patterns Of Order 4, Yubin Gao, Yanling Shao 2016 North University of China

Potentially Nilpotent Tridiagonal Sign Patterns Of Order 4, Yubin Gao, Yanling Shao

Electronic Journal of Linear Algebra

An $n\times n$ sign pattern ${\cal A}$ is said to be potentially nilpotent (PN) if there exists some nilpotent real matrix $B$ with sign pattern ${\cal A}$. In [M.~Arav, F.~Hall, Z.~Li, K.~Kaphle, and N.~Manzagol.Spectrally arbitrary tree sign patterns of order $4$, {\em Electronic Journal of Linear Algebra}, 20:180--197, 2010.], the authors gave some open questions, and one of them is the following: {\em For the class of $4 \times 4$ tridiagonal sign patterns, is PN (together with positive and negative diagonal entries) equivalent to being SAP?}\ In this paper, a positive answer ...


Bounds On The Expected Size Of The Maximum Agreement Subtree, Colby Long, Daniel Irving Bernstein, Lam Si Tung Ho, Mike Steel, Katherine St. John, Seth Sullivant 2016 The Ohio State University

Bounds On The Expected Size Of The Maximum Agreement Subtree, Colby Long, Daniel Irving Bernstein, Lam Si Tung Ho, Mike Steel, Katherine St. John, Seth Sullivant

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Exploring The Space Of Rna Secondary Structures, Heather C. Smith 2016 Georgia Institute of Technology

Exploring The Space Of Rna Secondary Structures, Heather C. Smith

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Markov Chains On Graphical Models Of Gene Regulation, Megan Bernstein 2016 Georgia Institute of Technology

Markov Chains On Graphical Models Of Gene Regulation, Megan Bernstein

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Genome Rearrangement: Graphs And Matrices, Jeffrey Davis 2016 Emory University

Genome Rearrangement: Graphs And Matrices, Jeffrey Davis

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


On The Expected Number Of Crossings In A Tanglegram, Eva Czabarka 2016 University of South Carolina

On The Expected Number Of Crossings In A Tanglegram, Eva Czabarka

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


On The Perfect Reconstruction Of The Structure Of Dynamic Networks, Alan Veliz-Cuba 2016 University of Dayton

On The Perfect Reconstruction Of The Structure Of Dynamic Networks, Alan Veliz-Cuba

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Spectral Graph Theory And New Stability Measures For Deterministic Gene Regulatory Networks, Fusun Akman, Devin Akman 2016 Illinois State University

Spectral Graph Theory And New Stability Measures For Deterministic Gene Regulatory Networks, Fusun Akman, Devin Akman

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Rogers-Ramanujan Computer Searches, James McLaughlin, Andrew Sills, Peter Zimmer 2016 West Chester University of Pennsylvania

Rogers-Ramanujan Computer Searches, James Mclaughlin, Andrew Sills, Peter Zimmer

James McLaughlin

We describe three computer searches (in PARI/GP, Maple, and Mathematica, respectively) which led to the discovery of a number of identities of Rogers–Ramanujan type and identities of false theta functions.


Preservers Of Term Ranks And Star Cover Numbers Of Symmetric Matrices, LeRoy B. Beasley 2016 Utah State University

Preservers Of Term Ranks And Star Cover Numbers Of Symmetric Matrices, Leroy B. Beasley

Electronic Journal of Linear Algebra

Let $\S$ denote the set of symmetric matrices over some semiring, $\s$. A line of $A\in\S$ is a row or a column of $A$. A star of $A$ is the submatrix of $A$ consisting of a row and the corresponding column of $A$. The term rank of $A$ is the minimum number of lines that contain all the nonzero entries of $A$. The star cover number is the minimum number of stars that contain all the nonzero entries of $A$. This paper investigates linear operators that preserve sets of symmetric matrices of specified term rank and sets of ...


Induced Subgraph Saturated Graphs, Craig M. Tennenhouse 2016 University of New England

Induced Subgraph Saturated Graphs, Craig M. Tennenhouse

Theory and Applications of Graphs

A graph $G$ is said to be \emph{$H$-saturated} if $G$ contains no subgraph isomorphic to $H$ but the addition of any edge between non-adjacent vertices in $G$ creates one. While induced subgraphs are often studied in the extremal case with regard to the removal of edges, we extend saturation to induced subgraphs. We say that $G$ is \emph{induced $H$-saturated} if $G$ contains no induced subgraph isomorphic to $H$ and the addition of any edge to $G$ results in an induced copy of $H$. We demonstrate constructively that there are non-trivial examples of saturated graphs for all ...


Improving Proof-Writing With Reading Guides, Mike Janssen 2016 Dordt College

Improving Proof-Writing With Reading Guides, Mike Janssen

Faculty Work: Comprehensive List

One of the barriers in the transition to advanced mathematics is that the proofs and ideas in even the best mathematics texts must be read more carefully than many students are accustomed to. Yet in order to learn to write proofs well, one must learn how to read proofs well. Borrowing an idea from Lewis Ludwig, I flipped my introduction to proofs (discrete structures) course in Spring 2016 with the use of reading guides. Each day, students were responsible for reading a section of the text and completing a worksheet that highlighted the main points, asked students to create their ...


Potentially Eventually Positive Star Sign Patterns, Yu Ber-Lin, Huang Ting-Zhu, Jie Cui, Deng Chunhua 2016 Huaiyin Institute of Technology

Potentially Eventually Positive Star Sign Patterns, Yu Ber-Lin, Huang Ting-Zhu, Jie Cui, Deng Chunhua

Electronic Journal of Linear Algebra

An $n$-by-$n$ real matrix $A$ is eventually positive if there exists a positive integer $k_{0}$ such that $A^{k}>0$ for all $k\geq k_{0}$. An $n$-by-$n$ sign pattern $\mathcal{A}$ is potentially eventually positive (PEP) if there exists an eventually positive real matrix $A$ with the same sign pattern as $\mathcal{A}$. An $n$-by-$n$ sign pattern $\mathcal{A}$ is a minimal potentially eventually positive sign pattern (MPEP sign pattern) if $\mathcal{A}$ is PEP and no proper subpattern of $\mathcal{A}$ is PEP. Berman, Catral, Dealba, et al. [Sign patterns that ...


Clustering-Based Robot Navigation And Control, Omur Arslan 2016 University of Pennsylvania

Clustering-Based Robot Navigation And Control, Omur Arslan

Departmental Papers (ESE)

In robotics, it is essential to model and understand the topologies of configuration spaces in order to design provably correct motion planners. The common practice in motion planning for modelling configuration spaces requires either a global, explicit representation of a configuration space in terms of standard geometric and topological models, or an asymptotically dense collection of sample configurations connected by simple paths, capturing the connectivity of the underlying space. This dissertation introduces the use of clustering for closing the gap between these two complementary approaches. Traditionally an unsupervised learning method, clustering offers automated tools to discover hidden intrinsic structures in ...


Combinatorics Of The Sonnet, Terry S. Griggs 2016 The Open University

Combinatorics Of The Sonnet, Terry S. Griggs

Journal of Humanistic Mathematics

Using a definition of a sonnet, the number of basic rhyming schemes is enumerated. This is then used to discuss the 86 sonnets which appear in John Clare's The Rural Muse.


Hybrid Proofs Of The Q-Binomial Theorem And Other Identities, Dennis Eichhorn, James McLaughlin, Andrew V. Sills 2016 University of California - Irvine

Hybrid Proofs Of The Q-Binomial Theorem And Other Identities, Dennis Eichhorn, James Mclaughlin, Andrew V. Sills

James McLaughlin

No abstract provided.


Polynomial Generalizations Of Two-Variable Ramanujan Type Identities, James McLaughlin, Andrew V. Sills 2016 West Chester University of Pennsylvania

Polynomial Generalizations Of Two-Variable Ramanujan Type Identities, James Mclaughlin, Andrew V. Sills

James McLaughlin

No abstract provided.


A New Summation Formula For Wp-Bailey Pairs, James McLaughlin 2016 West Chester University of Pennsylvania

A New Summation Formula For Wp-Bailey Pairs, James Mclaughlin

James McLaughlin

No abstract provided.


Graphs With Reciprocal Eigenvalue Properties, SWARUP KUMAR PANDA, Sukanta Pati 2016 IIT GUWAHATI

Graphs With Reciprocal Eigenvalue Properties, Swarup Kumar Panda, Sukanta Pati

Electronic Journal of Linear Algebra

In this paper, only simple graphs are considered. A graph G is nonsingular if its adjacency matrix A(G) is nonsingular. A nonsingular graph G satisfies reciprocal eigenvalue property (property R) if the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G) and G satisfies strong reciprocal eigenvalue property (property SR) if the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G) and they both have the same multiplicities. From the definitions property SR implies property R. Furthermore, for some classes of graphs (for ...


Digital Commons powered by bepress