L(2, 1)-Labeling of trapezoid graphs

Abstract

An L(2, 1)−labeling (L21L) of a graph G = (V, E) is an assignment f from the node-set V to the set {0, 1, 2, 3, . . .} so that adjoining nodes get numbers at least two apart, and nodes at distance two get different numbers. The L21L number λ2,1(G) is the difference between the greatest and least label used in the labeling process. In this paper, we have proved that, for a trapezoid graph (T G) G, the upper bound of λ2,1(G) ≤ 5∆ − 4, where ∆ is the maximum degree of the graph G. This paper also provides L21L of a simple triangle graph, a subclass of T G. We have shown that for a simple triangle graph, the upper bound of λ2,1(G) is 4∆.