AbstractsMathematics

Let d(u,v) denote the distance between two vertices u and v on a graph G and let diam(G) denote the diameter of such a graph G. A connected graph G has a radio labeling f if, for all vertices u, v of G, d(u,v) + |??(u) - ??(v)| ??? diam(G) + 1 (1) The span of the labeling function f is the maximum integer assigned by f. The radio number of a graph G, rn(G), is the minimum possible span obtained over all possible radio labelings of the graph G. A path graph Pn has n consecutive vertices along n ??? 1 consecutive edges. A grid graph is defined as the Cartesian product of two path graphs, and a square grid graph is obtained by taking the product of identical path graphs Pn Pn. In this paper, the radio number of all even grid graphs is determined using bounding techniques alone, while establishing fundamental guidelines for odd grids and distance-maximizing labelings, in general. Advisors/Committee Members: Wyels, Cynthia (committeeMember).