On the super connectivity of direct product of graphs

A vertex-cut S is called a super if G − disconnected and it contains no isolated vertices. The super-connectivity , κ ′, the minimum cardinality over all vertex-cuts. This article provides bounds for connectivity of direct product an arbitrary graph complete K n . Among other results, we show that non-complete with girth( ) = 3 ′( ∞, then × ≤ min{ mn 6, m ( 1) + 5, 5 8}, where | V )|