ON THE SIZE DEFICIENCY OF CYCLE GRAPHS AND SOME INTEGER SEQUENCES
JOHN RAFAEL M. ANTALAN *
Department of Mathematics and Physics, College of Arts and Sciences, Central Luzon State University, P.O.Box 3120,Science City of Mu~noz, Nueva Ecija, Philippines.
INGRID F. CALANNO
Department of Mathematics and Physics, College of Arts and Sciences, Central Luzon State University, P.O.Box 3120,Science City of Mu~noz, Nueva Ecija, Philippines.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Integer sequence, cycle graph, complete graph, size deficiency, sum of divisor, aliquot divisors, sum of aliquot divisors, perfect number, quasi-perfect number, almost perfect number, multiplyperfect number, perfectly sized deficient cycle and graph, quasi-perfectly sized deficient cyle and graph, almost-perfectly sized deficient cycle and graph, multiplyperfectly sized deficient cycle, square sized deficient cycle, Diophantine equation