Affiliation:
1. Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka 560029, India
Abstract
The eccentric graph of a graph [Formula: see text], denoted by [Formula: see text], is a derived graph with the vertex set same as that of [Formula: see text] and two vertices in [Formula: see text] are adjacent if one of them is an eccentric vertex of the other. The process of constructing iterative eccentric graphs, denoted by [Formula: see text] is called eccentrication. A graph [Formula: see text] is said to be [Formula: see text] if [Formula: see text] are the only non-isomorphic graphs, and the graph [Formula: see text] is isomorphic to [Formula: see text]. In this paper, we prove the existence of an [Formula: see text]-cycle for any simple graph. The importance of this result lies in the fact that the enumeration of eccentrication of a graph reduces to a finite problem. Furthermore, the enumeration of a corresponding sequence of graph parameters such as chromatic number, domination number, independence number, minimum and maximum degree, etc., reduces to a finite problem.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics
Cited by
1 articles.
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1. A Study on Exact Deg-Centric Graphs of Graphs;Journal of Interconnection Networks;2024-03-15