A Study On Set-Graphs
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10.5120/20754-3173 |
Johan Kok, K P Chithra, N K Sudev and C Susanth. Article: A Study On Set-Graphs. International Journal of Computer Applications 118(7):1-5, May 2015. Full text available. BibTeX
@article{key:article,
author = {Johan Kok and K. P. Chithra and N. K. Sudev and C. Susanth},
title = {Article: A Study On Set-Graphs},
journal = {International Journal of Computer Applications},
year = {2015},
volume = {118},
number = {7},
pages = {1-5},
month = {May},
note = {Full text available}
}
Abstract
A primitive hole of a graph G is a cycle of length 3 in G. The number of primitive holes in a given graph G is called the primitive hole number of that graph G. The primitive degree of a vertex v of a given graph G is the number of primitive holes incident on the vertex v. In this paper, we introduce the notion of set-graphs and study the properties and characteristics of set-graphs. We also check the primitive hole number of a set-graph and the primitive degree of its vertices. Interesting introductory results on the nature of order of set-graphs, degree of the vertices corresponding to subsets of equal cardinality, the number of largest complete subgraphs in a set-graph etc. are discussed in this study. A recursive formula to determine the primitive hole number of a set-graph is also derived in this paper.
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