Radio labeling of biconvex split graphs

Abstract

ABSTRACT A radio labeling of a graph G is a function f : V ( G ) → { 0 , 1 , … } such that for every pair of distinct vertices u , v ∈ V ( G ) , | f ( u ) − f ( v ) | ≥ 1 + diam ( G ) − d ( u , v ) , where diam(G) denotes the diameter of the graph and d(u, v) is the distance between the vertices u and v. The span of a radio labeling f of a graph G is the difference between the least and the largest labels assigned by f and is denoted by, span(f). The radio number of a graph G denoted by, rn(G), is the least positive integer s, such that there exists a radio labeling of G with span s. In this paper, we study the radio labeling of a special class of split graphs called biconvex split graphs of diameter three and we obtain both a lower bound and an upper bound for the radio number of biconvex split graphs of diameter three. Further, we determine the radio number of biconvex split graphs with three maximum degree vertices having disjoint independent neighbors.