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A Study On Set-Graphs

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International Journal of Computer Applications
© 2015 by IJCA Journal
Volume 118 - Number 7
Year of Publication: 2015
Authors:
Johan Kok
K. P. Chithra
N. K. Sudev
C. Susanth
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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