The split domination in arithmetic graphs

This paper highlights about the theory of domination in graphs, more specifically on the characteristics of the split domination number of an Arithmetic Graph and has obtained important results. The split domination of these arithmetic graphs have been studied as it enables us to construct graphs with a given split domination number in a simple way. We have obtained an upper bound for the split domination number of the Vm graph as r+1, where m is a positive integer and is the canonical representation, where are distinct primes and m = p₁^a₁, p₂^a₂. …. p_r^a_r, is the canonical representation, where, p1,p2,p3,….p_r are distinct primes and a_i’s >1.