L(2,1)-Labeling for Bloom Graph

Abstract

An $L(2,1)-$labeling of a graph is a function from the vertex set $V(G)$ to the set of all non-negative integers such that $\vert f(u)-f(v)\vert \ge 2 $ if and are vertices and $\vert f(u)-f(v)\vert \ge 1$ if $d(u,v)=2 $, where $d(u,v)$ denotes the distance between u and v in G. The $L(2,1)$-labeling number of G, denoted by $\lambda (G)$, is the smallest number k such that there is an $ L(2,1)$-labeling with maximum label k. In this paper we determine $ L(2,1)$-Labeling for Bloom Graph.