Call for Paper - June 2022 Edition
IJCA solicits original research papers for the June 2022 Edition. Last date of manuscript submission is May 20, 2022. Read More

A Study On Set-Graphs

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

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

	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}


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.


  • J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Macmillan Press, London, 1976.
  • G. Chartrand and L. Lesniak, Graphs and Digraphs, CRC Press, 2000.
  • J. T. Gross and J. Yellen, Graph Theory and its Applications, CRC Press, 2006.
  • S. S. Gupta and T. Liang, On a Sequential Subset Selection Procedure, Technical report #88-23, Department of Statistics, Purdue University, Indiana, U. S. , 1988.
  • F. Harary, Graph Theory, Addison-Wesley, 1994.
  • J. Kok and N. K. Sudev, A Study on Primitive Holes of Certain Graphs, International Journal of Scientific and Engineering Research, 6(3)(2015), 631-635.
  • J. Kok and Susanth C. , Introduction to the McPherson Number (G) of a Simple Connected Graph, Pioneer Journal of Mathematics and Mathematical Sciences, 13(2), (2015), 91- 102.
  • T. A. McKee and F. R. McMorris, Topics in Intersection Graph Theory, SIAM, Philadelphia, 1999.
  • K. H. Rosen, Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2000.
  • D. B. West, Introduction to Graph Theory, Pearson Education Inc. , 2001.