A Study On Set-Graphs
Johan Kok, K. P. Chithra, Sudev Naduvath, C Susanth · International Journal of Computer Applications · 2015
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.