Further results on k-sequential graphs (Q1114714)

Given a (p,q)-graph G and a positive integer k, a k-sequential numbering of G is an assignment of distinct numbers \(k,k+1,k+2,...,k+p+q-1\) to be \(p+q\) elements of G so that every edge \(u_{\nu}\) of G receives the absolute difference of the numbers assigned to the vertices \(\mu\) and \(\nu\). G is then called k-sequential if it admits such an assignment of numbers on its vertices. In this paper, a new necessary condition for a graph to be k-sequential is obtained and this result turns out to be a generalization of an earlier result of Slater. Also, several classes of graphs are shown to be k-sequential for various values of k hitherto unknown.