A note on the connectivity of direct products of graphs. (18th August 2018)

• Record Type: Journal Article
• Authors: Zhihui, Ma; Xianglan, Cao
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 21:Number 6(2018)
• Page Start: 1347
• Page End: 1352
• Publication Date: 2018-08-18
• Subjects: Edge connectivity -- Bipartite graph -- Edge-separating set -- Diret product; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2018.1530175
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: In recent years, the vertex connectivity and edge connectivity have aroused great interest of many scholars in the field of mathematics. We consider in this note that edge connectivity of a graph called k ′( G ). In this note, If G is a bipartite graph with vertices n ≥ 3 we prove that k ′( G × Kn ) = min { n ( n – 1) k ′( G ), ( n – 1) δ ( G )}, and their edge connectivity is satisfied k ′( G ) = δ ( G ), we can obtain k ′( G × Kn ) = δ ( G × Kn ) = ( n – 1) δ ( G ).