A note on indices of primepower and semiprime divisor function graph

Abstract

The notion of using number theortic based graph seems to be one of the flourishing areas in Graph theory. One such concept is the divisor function graph GD(n) which is defined as: For any positive integer n ≥ 1 with r divisors d1, d2, d3, ..., dr, divisor function graph GD(n) is a (V, E) graph with V as the set of all factors of n and E be defined in such a way that two vertices di and dj are adjacent if and only if either di | dj or dj | di, i 6= j. In this paper, we analyze the operation sum of two divisor function graphs and investigate several indices exclusively for prime powers and for semi primes. Also, we derive a result for an independent function.