Super connectivity of lexicographic product graphs

TL;DR

This paper investigates the super connectivity and $k_{1}$-connectivity of lexicographic product graphs, providing bounds and insights into their structural robustness.

Contribution

It introduces bounds for super connectivity and $k_{1}$-connectivity specifically for lexicographic product graphs, advancing understanding of their fault tolerance.

Findings

Bounds established for super connectivity of lexicographic product graphs.

Bounds established for $k_{1}$-connectivity of lexicographic product graphs.

Enhanced understanding of the structural robustness of these graph products.

Abstract

For a graph $G$, $k(G)$ denotes its connectivity. A graph is super connected if every minimum vertex-cut isolates a vertex. Also $k_{1}$-connectivity of a connected graph is the minimum number of vertices whose deletion gives a disconnected graph without isolated vertices. This paper provides bounds for the super connectivity and $k_{1}$-connectivity of the lexicographic product of two graphs.