The generalized 4-connectivity of godan graphs

TL;DR

This paper investigates the generalized 4-connectivity of godan graphs, a type of Cayley graph, establishing that it equals n-1 for all n ≥ 3, which enhances understanding of their network robustness.

Contribution

The paper determines the exact generalized 4-connectivity of godan graphs, extending the theoretical knowledge of their structural properties.

Findings

a_n has a_n-1 generalized 4-connectivity for n 3.

Provides new insights into the connectivity properties of Cayley graphs.

Enhances understanding of network robustness in interconnection networks.

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 godan graph $EA_n$ is a kind of Cayley graphs which posses many desirable properties. In this paper, we shall study the generalized 4-connectivity of $EA_n$ and show that $\kappa_4(EA_n)=n-1$ for $n\ge 3$.