THE L(2,1)-LABELING ON TOTAL GRAPHS OF COMPLETE BIPARTITE GRAPHS

摘要

An L(2, l)-labeling of a connected graph G is denned as a function / from the vertex set V(G) to the set of all nonnegative integers such that | f(u)- f(v)|≧ 2 if d_g(u,v) = 1 and | f(u)- f(v)|≧1 if d_g(u,v) = 2, where d_G(u,v) denotes the distance between vertices u and v in G. The L(2, l)-labeling number of G, denoted by A(G), is the smallest number k such that G has an L(2, l)-labeling with max{ f(v) : v ∈V(G)} = k. In this paper, we consider the total graphs of the complete bipartite graphs and provide exact value for their A-numbers.