Component Connectivity of 3-Ary n -Cubes
Uday Jagadale, Amruta Shinde, Prashant Malavadkar · International Journal of Foundations of Computer Science · 2025
For an integer [Formula: see text], the r-component connectivity of a connected graph G, denoted by [Formula: see text], is the minimum number of vertices whose removal results in a graph with at least r components. In this paper, we extend the result on r-component connectivity of k-ary n-cubes for [Formula: see text] established by Lv et al. [M. Lv, J. Fan, J. Zhou et al., The reliability of k-ary n-cube based on component connectivity, Comput. J. 65(8) (2022) 2197–2208], to 3-ary n-cubes. We show that the [Formula: see text]-component connectivity of 3-ary n-cubes is [Formula: see text] for integers r and n satisfying [Formula: see text].