The generalized 3-connectivity of burnt pancake graphs and godan graphs

TL;DR

This paper investigates the generalized 3-connectivity of burnt pancake graphs and godan graphs, showing both have a connectivity of n-1, which is significant for their application in interconnection networks.

Contribution

It establishes the exact generalized 3-connectivity values for burnt pancake graphs and godan graphs, expanding understanding of their structural robustness.

Findings

3-connectivity of BP_n is n-1

3-connectivity of EA_n is n-1

Both graphs have high connectivity suitable for network applications

Abstract

The generalized $k$-connectivity of a graph $G$, denoted by $\kappa_k(G)$, is the minimum number of internally edge disjoint $S$-trees for any $S\subseteq V(G)$ and $|S|=k$. The generalized $k$-connectivity is a natural extension of the classical connectivity and plays a key role in applications related to the modern interconnection networks. The burnt pancake graph $BP_n$ and the godan graph $EA_n$ are two kinds of Cayley graphs which posses many desirable properties. In this paper, we investigate the generalized 3-connectivity of $BP_n$ and $EA_n$. We show that $\kappa_3(BP_n)=n-1$ and $\kappa_3(EA_n)=n-1$.