Abstract

The average connectivity κ􀴤(G) = ΣκG(u,v)u,v􀵫ʋ2􀵯,κG(u, v)is defined to be the maximum value of k for which u and v are k-connected. In this paper, we consider the concept of the average connectivity of an arithmetic graph. It is shown that κ􀴤(G) ≤ 􁉂(ʋ−2)􁉀ʋ−β2􁉁+(ʋ−β)􁉀β2􁉁+(ʋ−β)2β􁉃􀵫ʋ2􀵯 where ν is the order and β is an independence number of an arithmetic graph. Also, it is clear that, if a1is increasing then κ􀴤(G) is decreasing for an arithmetic graph G = Vn, where n =P1a1×P2 .

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