2017/05/23 by Hui Gao, Gao, Hui, Benjian Lv +3
Computer Science · Materials Science · #Advanced Graph Theory Research #Carbon and Quantum Dots Applications #Combinatorics (math.CO) #FOS: Mathematics #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.1705.08087
openalex publication_date 2017/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The generalized k-connectivity κk(G) of a graph G, which was introduced by Chartrand et al.(1984) is a generalization of the concept of vertex connectivity. Let G and H be nontrivial connected graphs. Recently, Li et al. gave a lower bound for the generalized 3-connectivity of the Cartesian product graph G \square H and proposed a conjecture for the case that H is 3-connected. In this paper, we give two different forms of lower bounds for the generalized 3-connectivity of Cartesian product graphs. The first lower bound is stronger than theirs, and the second confirms their conjecture.