Physical Sciences and Mathematics Commons^™

Strategies Community College Mexican American Adult College Algebra Students Use When Graphing Function Transformations, Roxana Pamela Jimenez

Theses and Dissertations

This qualitative case study pursued to describe the different strategies Mexican American adult students in a local community college used to graph function transformations. Participants in the study were purposefully selected using a criterion sampling to ensure participants were atypical, above average students between the ages 18-22, and had a final course average of 89.5-100 in College Algebra. Three research questions were examined 1) In what ways do Mexican American adult college students graph a function transformation? 2) Which strategies do students implement when graphing a function transformation? Qualitative research methods using think aloud semi-structured interviews were used in this …

Structure Of A Total Independent Set, Lewis Stanton

Rose-Hulman Undergraduate Mathematics Journal

Let $G$ be a simple, connected and finite graph with order $n$. Denote the independence number, edge independence number and total independence number by $\alpha(G), \alpha'(G)$ and $\alpha''(G)$ respectively. This paper establishes an upper bound for $\alpha''(G)$ in terms of $\alpha(G)$, $\alpha'(G)$ and $n$. We also describe the possible structures for a total independent set containing a given number of elements.

Cohen-Macaulay Properties Of Closed Neighborhood Ideals, Jackson Leaman

All Theses

This thesis investigates Cohen-Macaulay properties of squarefree monomial ideals, which is an important line of inquiry in the field of combinatorial commutative algebra. A famous example of this is Villareal’s edge ideal [11]: given a finite simple graph G with vertices x1, . . . , xn, the edge ideal of G is generated by all the monomials of the form xixj where xi and xj are adjacent in G. Villareal’s characterization of Cohen-Macaulay edge ideals associated to trees is an often-cited result in the literature. This was extended to chordal and bipartite graphs by Herzog, Hibi, and Zheng in …

Matroid Generalizations Of Some Graph Results, Cameron Crenshaw

LSU Doctoral Dissertations

The edges of a graph have natural cyclic orderings. We investigate the matroids for which a similar cyclic ordering of the circuits is possible. A full characterization of the non-binary matroids with this property is given. Evidence of the difficulty of this problem for binary matroids is presented, along with a partial result for binary orderable matroids.

For a graph G, the ratio of |E(G)| to the minimum degree of G has a natural lower bound. For a matroid M that is representable over a finite field, we generalize this to a lower bound on …

Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic

Turkish Journal of Mathematics

This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph, and the last is the graph-associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs. In the last section, we study some properties related to $\mathcal{H}$-polytopes.

Supra-Approximation Spaces Using Combined Edges Systems, Hussein R. Jaffer, Khalid Sh. Al’Dzhabri

Al-Qadisiyah Journal of Pure Science

The primary in this paper's notion, the i-space using incident edges system (resp. n-space using non-incidental edges system), is what this study is responsible for generating and investigating. Additionally, we used c-interior to define the c-lower approximations in generalized rough set theory (resp. i-interior and n-interior) Additionally, the c-upper approximations are defined using c-closure (as opposed to i-closure and n-closure), and some of its characteristics are studied.

2-Uniform Covering Groups Of Elementary Abelian 2-Groups, Dana Saleh, Rachel Quinlan

All Works

This article is concerned with the classification of Schur covering groups of the elementary abelian group of order (Formula presented.), up to isomorphism. We consider those covering groups possessing a generating set of n elements having only two distinct squares. We show that such groups may be represented by 2-vertex-colored and 2-edge-colored graphs of order n. We show that in most cases, the isomorphism type of the group is determined by that of the 2-colored graph, and we analyze the exceptions.

Opposite Trees, Theo Goossens

Theses and Dissertations (Comprehensive)

A spanning tree of a graph G is a connected acyclic subgraph of G that includes all of the vertices in G. The degree of a vertex is the number of edges incident to that vertex. Given a spanning tree T of a graph G, an opposite tree of T is a spanning tree of G where the degree of each of its vertices is different from its degree in T. For complete, complete bipartite, and complete multipartite graphs, we give the conditions spanning trees of these graphs must satisfy in order to have an opposite tree.