ON THE SIZE DEFICIENCY OF CYCLE GRAPHS AND SOME INTEGER SEQUENCES

We define the size deficiency of a simple graph G to be the number of edges needed to complete G. In this simple research note we generate some integer sequences from size deficiency of cycle graphs Cn by determining the values of n for which Cn has size deficiency equal to n, n + 1, n - 1, kn and k2 where n and k are positive integers and extend this to simple connected graph. The choices for n, n + 1, n - 1, kn and k2 as the value of size deficiency for Cn were carefully chosen so that relation to some concepts attached to the sum of divisor function σ(n) of a positive integer n will be established.