Abstract:

Given a (p,q) graph G and positive integer k, an k sequentially additive numbering of G is an assignment of distinct numbers k,k+1,…,k+p+q-1,  to the p+q elements of G such that every edge uv of G receives the sum  of the numbers assigned to the vertices u and v. A graph which admits such an assignment to its  elements is called an k sequentially additive graph. In this paper, the authors give some  structural properties on sequentially additive graph, and a construction of inf inite families of k sequentially additive graphs.

Key words: Graph, Numbering, Construction, Sequentially additive