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 Faculty Publications 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/. Creator An entity primarily responsible for making the resource Raja, Manakkulam Rohith; Mangam, Tabitha Agnes; Kok, Johan; Naduvath, Sudev Title A name given to the resource Cyclic property of iterative eccentrication of trees Date A point or period of time associated with an event in the lifecycle of the resource 01-01-2025 Source A related resource from which the described resource is derived Asian-European Journal of Mathematics;Volume;18;Issue;10;Article No.;2550043; Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1142/S1793557125500433" target="_blank" rel="noreferrer noopener">https://doi.org/10.1142/S1793557125500433</a> <br /><br /><a href="https://www.scopus.com/pages/publications/105005017097?origin=resultslist" target="_blank" rel="noreferrer noopener">https://www.scopus.com/pages/publications/105005017097?origin=resultslist</a> 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 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 Description An account of the resource 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. Subject The topic of the resource eccentric graph; eccentrication; Eccentricity; iterative eccentric graphs; ?-cycle Publisher An entity responsible for making the resource available World Scientific Relation A related resource ISSN: 17935571; Language A language of the resource English Type The nature or genre of the resource Article Rights Information about rights held in and over the resource Restricted Access; Hardcopy may be available in the library Format The file format, physical medium, or dimensions of the resource online