L(2,1)-labelings of the edge-multiplicity-paths-replacement of a graph

摘要

An L(2,1)-labeling of a graph is an assignment of nonnegative integers to such that the difference between labels of adjacent vertices is at least , and the difference between labels of vertices that are distance two apart is at least 1. The span of an L(2,1)-labeling of a graph is the difference between the maximum and minimum integers used by it. The minimum span of an L(2,1)-labeling of is denoted by . This paper focuses on L(2,1)-labelings-number of the edge-multiplicity-paths-replacement of a graph . In this paper, we obtain that , for ; and , for any graph with maximum degree . And the L(2,1)-labelings-numbers of the edge-multiplicity-paths-replacement are completely determined for . And we show that the class of graphs with satisfies the conjecture: by Havet and Yu (Technical Report 4650, 2002).