Physical Sciences and Mathematics Commons^™

Radio Number For Fourth Power Paths, Linda V. Alegria

Electronic Theses, Projects, and Dissertations

A path on n vertices, denoted by Pn, is a simple graph whose vertices can be ordered so that two vertices are adjacent if and only if they are consecutive in the order. A fourth power path, Pn4, is obtained from Pn by adding edges between any two vertices, u and v, whose distance in Pn, denoted by dPn(u,v), is less than or equal to four. The diameter of a graph G, denoted diam(G) is the greatest distance between any two distinct vertices of G. A radio labeling of a graph G is a function f that assigns to each …