Physical Sciences and Mathematics Commons^™

A Study Of Graphical Permutations, Jessica Thune

UNLV Theses, Dissertations, Professional Papers, and Capstones

A permutation π on a set of positive integers {a_1,a_2,...,a_n} is said to be graphical if there exists a graph containing exactly a_i vertices of degree (a_i) for each i. It has been shown that for positive integers with a_1

Generalizations Of Pascal's Triangle: A Construction Based Approach, Michael Anton Kuhlmann

UNLV Theses, Dissertations, Professional Papers, and Capstones

The study of this paper is based on current generalizations of Pascal's Triangle, both the expansion of the polynomial of one variable and the multivariate case. Our goal is to establish relationships between these generalizations, and to use the properties of the generalizations to create a new type of generalization for the multivariate case that can be represented in the third dimension.

In the first part of this paper we look at Pascal's original Triangle with properties and classical applications. We then look at contemporary extensions of the triangle to coefficient arrays for polynomials of two forms. The first of …

Zero-Sum Magic Graphs And Their Null Sets, Samuel M. Hansen

UNLV Theses, Dissertations, Professional Papers, and Capstones

For any element h of the Natural numbers, a graph G=(V,E), with vertex set V and edge set E, is said to be h-magic if there exists a labeling of the edge set E, using the integer group mod h such that the induced vertex labeling, the sum of all edges incident to a vertex, is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h for which G admits a zero-sum h-magic labeling. A graph G is said to be uniformly …