Super connectivity of a family of direct product graphs. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Soliemany, F.; Ghasemi, M.; Varmazyar, R.
• Is Part Of: International journal of computer mathematics. Volume 7:Issue 1(2022)
• Page Start: 1
• Page End: 5
• Publication Date: 2022-01-02
• Subjects: Direct product -- super connectivity -- separating set; 05C40 -- 05C90; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2021.1974567
• Languages: English
• ISSNs: 2379-9927

Abstract

Abstract : Let G 1 and G 2 be two graphs. The Kronecker product G 1 × G 2 has vertex set V ( G 1 × G 2 ) = V ( G 1 ) × V ( G 2 ) and the edge set E ( G 1 × G 2 ) = { ( u 1, v 1 ) ( u 2, v 2 ) ∣ u 1 u 2 ∈ E ( G 1 ), v 1 v 2 ∈ E ( G 2 ) } . In this paper we show that if K p 1, p 2, …, p r is a complete multipartite graph, where the parameters p 1, p 2, …, p r satisfying certain conditions and P n is a path of length n −1, then K p 1, p 2, …, p r × P n is not super i -connected, where 1 ≤ i ≤ n − 1 and n ≥ 2 . Also we show that K p 1, p 2, …, p r × C n is not super connected, where C n is a cycle of length n and n ≥ 3 .