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arXiv · 2310.00878

The generalized 4-connectivity of burnt pancake graphs

Jing Wang·Jiang Wu·Zhangdong Ouyang·Yuanqiu Huang
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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. An $n$-dimensional burnt pancake graph $BP_n$ is a Cayley graph which posses many desirable properties. In this paper, we try to evaluate the reliability of $BP_n$ by investigating its generalized 4-connectivity. By introducing the notation of inclusive tree and by studying structural properties of $BP_n$, we show that $\kappa_4(BP_n)=n-1$ for $n\ge 2$, that is, for any four vertices in $BP_n$, there exist ($n-1$) internally edge disjoint trees connecting them in $BP_n$.

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Jing Wang, Jiang Wu, Zhangdong Ouyang, Yuanqiu Huang. 2023-10-02. The generalized 4-connectivity of burnt pancake graphs. https://arxiv.org/abs/2310.00878

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