Cyclic property of iterative eccentrication of a graph

Title

Cyclic property of iterative eccentrication of a graph

Creator

Raja M.R.; Kok J.; Mangam T.A.; Naduvath S.

Description

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 constructing iterative eccentric graphs, denoted by Gek is called 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 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. 2023 World Scientific Publishing Company.

Source

Discrete Mathematics, Algorithms and Applications, Vol-15, No. 7

Date

2023-01-01

Publisher

World Scientific

Subject

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

Coverage

Raja M.R., Department of Mathematics, Christ (Deemed to Be University), Karnataka, Bangalore, 560029, India; Kok J., Department of Mathematics, Christ (Deemed to Be University), Karnataka, Bangalore, 560029, India; Mangam T.A., Department of Mathematics, Christ (Deemed to Be University), Karnataka, Bangalore, 560029, India; Naduvath S., Department of Mathematics, Christ (Deemed to Be University), Karnataka, Bangalore, 560029, India

Rights

Restricted Access

Relation

ISSN: 17938309

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S1793830922501555

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