Neighbor connectivity of $k$-ary $n$-cubes

TL;DR

This paper determines the neighbor connectivity of $k$-ary $n$-cubes, a measure of network robustness, for all dimensions and degrees, providing insights into network failure impacts.

Contribution

It provides a complete characterization of neighbor connectivity for $k$-ary $n$-cubes across all parameters, filling a gap in network topology analysis.

Findings

Neighbor connectivity of $k$-ary $n$-cubes is fully characterized.

Results apply to all $n \\ge1$ and $k \\ge2$.

Implications for network robustness and failure analysis.

Abstract

The neighbor connectivity of a graph $G$ is the least number of vertices such that removing their closed neighborhoods from $G$ results in a graph that is disconnected, complete or empty. If a~graph is used to model the topology of an interconnection network, this means that the failure of a network node causes failures of all its neighbors. We completely determine the neighbor connectivity of $k$-ary $n$-cubes for all $n\ge1$ and $k\ge2$.