\(i\)-Connectivity in a Generalized Hypercube

Linda M. Lawson1, James W. Boland1, Richard D. Ringeisen 2
1Department of Mathematics East Tennessee State University Johnson City, TN 37614
2East Carolina University Greenville, NC 27858

Abstract

Inclusive connectivity parameters for a given vertex in a graph \(G\) are measures of how close that vertex is to being a cutvertex. Thus they provide a local measure of graph vulnerability. In this paper we provide bounds on the inclusive connectivity parameters in \(K_2 \times G\) and inductively extend the results to a certain generalized hypercube.