L(2,1)-Labeling: An Algorithmic Approach to Cycle Dominated Graphs

Abstract

Let G be a connected, undirected graph. Distance two labeling or a L(2,1)-labeling of a graph G is an assignment f from the vertex set V (G) to the set of non- negative integers such that |f(x)− f(y)| is greater than or equal to 2 if x and y are adjacent and |f(x) − f(y)| is greater than or equal to 1 if x and y are at distance 2, for all x and y in V (G). The L(2,1)-labeling number (Lamda)(G) of G is the smallest number k such that G has an L(2,1)-labeling f with max {f(v) : v 2 V (G) }is equal to k. In this paper, we present algorithms to get L(2,1)-labeling of cycle dominating graphs like Diamond graphs, nC4 with a common vertex and Books Bn and hence we find the (lamda)- number of these graphs. Keywords: Channel assignment; transmitters; L(2,1)-labeling; Books; Distance two labeling 2010 Mathematics Subject Classification: 05C78.