Super spanning connectivity of the generalized hypercube network

Abstract

The generalized hypercube $G(m_1,m_2,\dots ,m_n)$ is one of the key interconnection networks with attractive topological properties. In this paper, we focus our attention on the super spanning connectivity of $G(m_1,m_2,\dots ,m_n)$. We show that for a pair of arbitrary nodes x and y in $G(m_1,m_2,\dots ,m_n)(m_i\ge 3,i=1,2,\dots ,n)$, there is a set of $s(1\le s\le \kappa (G(m_1,m_2,\dots ,m_n)\left)\right)$ internally node-disjoint $x,y$-paths whose union covers every vertex in $G(m_1,m_2,\dots ,m_n)$, where $\kappa \left(G\right(m_1,m_2,\dots ,m_n\left)\right)$ denotes the connectivity of $G(m_1,m_2,\dots ,m_n)$. Our results, in some sense, extended a previous result in Shih and Kao (2011) [23].