ON THE SIZE DEFICIENCY OF CYCLE GRAPHS AND SOME INTEGER SEQUENCES

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Published: 2016-03-12

Page: 192-200


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 for which Cn has size deficiency equal to n, n + 1, - 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


How to Cite

M. ANTALAN, J. R., & CALANNO, I. F. (2016). ON THE SIZE DEFICIENCY OF CYCLE GRAPHS AND SOME INTEGER SEQUENCES. Asian Journal of Mathematics and Computer Research, 11(3), 192–200. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/447

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