**June 22, 2020**. Read More

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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