P_k and C_k structure and substructure connectivity of hypercubes

16 Jun 2020
•
Chen Yihan
•
Zhang Bicheng

Hypercube is one of the most important networks to interconnect processors in
multiprocessor computer systems. Different kinds of connectivities are
important parameters to measure the fault tolerability of networks...Lin et
al.\cite{LinStructure} introduced the concept of $H$-structure connectivity
$\kappa(Q_n;H)$ (resp. $H$-substructure connectivity $\kappa^s(Q_n;H)$) as the
minimum cardinality of $F=\{H_1,\dots,H_m\}$ such that $H_i (i=1,\dots,m)$ is
isomorphic to $H$ (resp. $F=\{H'_1,\dots,H'_m\}$ such that $H'_i (i=1,\dots,m)$
is isomorphic to connected subgraphs of $H$) such that $Q_n-V(F)$ is
disconnected or trivial. In this paper, we discuss $\kappa(Q_n;H)$ and
$\kappa^s(Q_n;H)$ for hypercubes $Q_n$ with $n\geq 3$ and $H\in \{P_k,C_k|3\leq
k\leq 2^{n-1}\}$. As a by-product, we solve the problem mentioned in
\cite{ManeStructure}.(read more)