The Connectivity Number of an Arithmetic Graph

The arithmetic graph Vn is defined as a graph with its vertex set is the set consists of the divisors of n (excluding 1) where n is a positive integer and ... where p'is are distinct primes and ai's ≥ 1 and two distinct vertices a, b which are not of the same parity are adjacent in this graph if (a, b) = pi, for some i, 1 ≤ i ≤ r. In this paper, we study some results related to the connectivity κ of an arithmetic graph. It is also shown that, the edge connectivity κ and the connectivity κ are equal in arithmetic graph Vn.