Cyclic property of iterative eccentrication of trees

Title

Cyclic property of iterative eccentrication of trees

Creator

Raja, Manakkulam Rohith; Mangam, Tabitha Agnes; Kok, Johan; Naduvath, Sudev

Description

A tree graph is an acyclic graph. The eccentric graph of a graph G, denoted by Ge is a derived graph with the vertex set same as that of G and two vertices in Ge are adjacent if one of them is an eccentric vertex of the other. The process of finding eccentric graph of a graph is called eccentrication and that of constructing iterative eccentric graphs, denoted by Gek, is called iterative eccentrication. A graph G is said to be ?-cyclic(t,l) if G, Ge, Ge2,?, Gek, Gek+1,?, Gek+l are the only non-isomorphic graphs, and the graph Gek+l+1 is isomorphic to Gek. In this paper, we prove the existence of an ?-cycle for any tree graph on n vertices. We also obtain some important results on eccentric graphs of trees. Then, we present a conjecture on the cyclic property of eccentrication of a general graph G. Finally, an analogy between the concept of ?-cycle for a graph and the dichotomy of the Riemann sphere into Fatou sets and Julia sets is presented. We also state some open problems in the area. 2025 World Scientific Publishing Company.

Source

Asian-European Journal of Mathematics;Volume;18;Issue;10;Article No.;2550043;

Date

01-01-2025

Publisher

World Scientific

Subject

eccentric graph; eccentrication; Eccentricity; iterative eccentric graphs; ?-cycle

Coverage

Raja M.R., Department of Mathematics, Christ University, Bangalore, India; Mangam T.A., Department of Mathematics, Christ University, Bangalore, India; Kok J., Department of Mathematics, Christ University, Bangalore, India; Naduvath S., Department of Mathematics, Christ University, Bangalore, India

Rights

Restricted Access; Hardcopy may be available in the library

Relation

ISSN: 17935571;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S1793557125500433

https://www.scopus.com/pages/publications/105005017097?origin=resultslist