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 $f:V\to \{0,1,2,\dots ,p-1\}$ 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.