More on Classes of Strongly Indexable Graphs

Abstract

Given any positive integer $k$, a $(p,q)$-graph $G = (V, E)$ is \emph{strongly $k$-indexable} if there exists a bijection $f:V \rightarrow \{0, 1, 2, \dots, p-1\}$ such that $f^+(E(G)) = \{k, k+1, k+2, \dots, k+q-1,\}$ where $f^+(uv) = f(u) + f(v)$ for any edge $uv \in E$; in particular, $G$ is said to be \emph{strongly indexable} when $k = 1$. For any strongly $k$-indexable $(p,q)$-graph $G, \ q \le 2p-3$ and if, in particular, $q = 2p-3$ then $G$ is called a \emph{maximal strongly indexable graph}. In this paper,  our main focus is to construct more classes of  $k$-strongly indexable graphs.