L(0, 1)-Labelling of Trapezoid Graphs

Abstract

L(0, 1)-labelling of a graph $$G=(V,E)$$ is a function f from the vertex set V(G) to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The L(0, 1)-labelling number denoted by $$\lambda _{0,1}(G)$$ of G is the minimum range of labels over all such labelling. In this article, it is shown that, for a trapezoid graph G with maximum vertex degree $$\Delta $$ , the upper bound of $$\lambda _{0,1}(G)$$ is $$\Delta -1$$ .