Combinatorics and Graph Theory


The Eigen-Complete Difference Ratio of Classes of Graphs Domination, Asymptotes and Area

Authors: Paul August Winter, Samson Ojako Dickson

The energy of a graph is related to the sum of -electron energy in a molecule represented by a molecular graph and originated by the HMO (Hückel molecular orbital) theory. Advances to this theory have taken place which includes the difference of the energy of graphs and the energy formation difference between and graph and its decomposable parts. Although the complete graph does not have the highest energy of all graphs, it is significant in terms of its easily accessible graph theoretical properties and has a high level of connectivity and robustness, for example. In this paper we introduce a ratio, the eigen-complete difference ratio, involving the difference in energy between the complete graph and any other connected graph G, which allows for the investigation of the effect of energy of G with respect to the complete graph when a large number of vertices are involved. This is referred to as the eigen-complete difference domination effect. This domination effect is greatest negatively (positively), for a strongly regular graph (star graphs with rays of length one), respectively, and zero for the lollipop graph. When this ratio is a function f(n), of the order of a graph, we attach the average degree of G to the Riemann integral to investigate the eigen-complete difference area aspect of classes of graphs. We applied these eigen-complete aspects to complements of classes of graphs.

Comments: 22 Pages.

Download: PDF

Submission history

[v1] 2015-02-17 06:44:25

Unique-IP document downloads: 83 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus