Virginia State University

Title: Iterations of Eccentric Diagraphs

Director(s): Dawit Haile, Department of Mathematics

Dates of Program: May 17, 2004 - June 28, 2004

Summary: This project is a study in graph theory and computational geometry. A directed graph (or diagraph) G = G(V, E) consists of a vertex set V(G) and an arc set E(G) = {(v,u) : v,u â?¬ V(G)}. The least number of areas in a diagraph G from vertex v to vertex u is the distance from v to u, denoted d_g(v,u) or simply d(v,u). The eccentricity e(v) of a vertex v is the maximum distance from v to any other vertex in G. Vertex u is an eccentric vertex of v if d(v,u) = e(v). The eccentric diagraph of G, denoted ED(G), is the diagraph on vertex set V(G) and with arc from vertex v to vertex u in ED(G) if and only if u is an eccentric vertex of v. This program will utilize this knowledge to investigate graph theoretic properties and find necessary and sufficient conditions for a diagraph to be an eccentric diagraph. In addition, research was also done on Permutation Matrix, Maximal Planar Graphs, and a Survey on RSA Encryption.

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