A Study on Set-Graphs

Johan Kok; K. P. Chithra; N. K. Sudev; C. Susanth

doi:10.5120/20754-3173

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arXiv · 1504.02703

A Study on Set-Graphs

Johan Kok·K. P. Chithra·N. K. Sudev·C. Susanth

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Abstract

A \textit{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 and primitive degree of set-graphs. 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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BibTeX RIS

Johan Kok, K. P. Chithra, N. K. Sudev, C. Susanth. 2015-04-09. A Study on Set-Graphs. https://doi.org/10.5120/20754-3173

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