Super connectivity of a family of direct product graphs. Issue 1 (2nd January 2022) - Soliemany, F.; Ghasemi, M.; Varmazyar, R.
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 .