Super connected and hyper connected arithmetic graphs

Abstract

A connected graph G is said to be super connected if every minimum vertex-cut isolates a vertex of G. Moreover a graph is said to be hyper connected if for every minimum vertex cut S, G − S has exactly two components, one of which is an isolated vertex. In this paper, we focussed the concept in arithmetic graphs V n and proved that, for an arithmetic graph G = V n , n = P a 1 1 × P a 2 2 × .... × P a r r where 0 < a i ≤ 2 and r > 3 is super and hyper connected and for at least one a i ≥ 3, the graph G = V n is only super connected. Also, it is clear that for every arithmetic graph G = V n , n is any integer is super and hyper edge connected.