Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Articles Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Cyclic property of iterative eccentrication of a graph Subject The topic of the resource eccentric graph; eccentrication; Eccentricity; iterative eccentric graphs; ?-cycle Description An account of the resource 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. Creator An entity primarily responsible for making the resource Raja M.R.; Kok J.; Mangam T.A.; Naduvath S. Source A related resource from which the described resource is derived Discrete Mathematics, Algorithms and Applications, Vol-15, No. 7 Publisher An entity responsible for making the resource available World Scientific Date A point or period of time associated with an event in the lifecycle of the resource 2023-01-01 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1142/S1793830922501555" target="_blank" rel="noreferrer noopener">https://doi.org/10.1142/S1793830922501555</a> <br /><br /><a href="https://www.scopus.com/inward/record.uri?eid=2-s2.0-85166097494&amp;doi=10.1142%2FS1793830922501555&amp;partnerID=40&amp;md5=36936af91b5c79ff02d8fc829e21e351" target="_blank" rel="noreferrer noopener">https://www.scopus.com/inward/record.uri?eid=2-s2.0-85166097494&amp;doi=10.1142%2fS1793830922501555&amp;partnerID=40&amp;md5=36936af91b5c79ff02d8fc829e21e351</a> Rights Information about rights held in and over the resource Restricted Access Relation A related resource ISSN: 17938309 Format The file format, physical medium, or dimensions of the resource Online Language A language of the resource English Type The nature or genre of the resource Article Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant 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