Connectivity of Double Graphs

TL;DR

This paper investigates the connectivity properties of double graphs formed via the Kronecker product, providing conditions under which they are maximally vertex- and edge-connected.

Contribution

It introduces sufficient conditions for double graphs to achieve maximum vertex and edge connectivity, advancing understanding of their structural robustness.

Findings

Double graphs can be maximally vertex-connected under certain conditions.

Double graphs can be maximally edge-connected under certain conditions.

Provides theoretical criteria for connectivity in double graphs.

Abstract

The double graph of a graph $G$ is defined as $\mathcal{D}[G]$ = $G \times T_2$, where \(T_2\) is the total graph with 2 vertices and $\times$ stands for the Kronecker product of graphs. In this paper, sufficient conditions for double graphs to be maximum vertex-connected, maximum edge-connected are presented.