Year: 2015
Type: article
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.
DOI: 10.5120/20754-3173
Authors: Johan Kok, K. P. Chithra, N. K. Sudev, C. Susanth
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W3104050049