EJGTAEJGTA

Electronic Journal of Graph Theory and Applications (EJGTA)Electronic Journal of Graph Theory and Applications (EJGTA)

A disconnected graph G is called a cluster if G is not union of K2s (1-factor) but union of complete graphs of order at least two. J. Akiyama, K. Ando and D. Avis showed in Lemma 2.1 of [2] that G is equi-eccentric if the eccentric graph Ge is a cluster or pK2. And they also characterized all graphs whose eccentric graphs are complete graphs and pK2 in [2]. In this paper, we determined in Theorem 2 all graphs whose eccentric graphs are clusters, which is an extension of Lemma 2.1 in [2].

The study successfully determined the characteristics of graphs whose eccentric graphs are clusters, revealing that such graphs must be complete n-partite graphs.The research extends previous work by Akiyama, Ando, and Avis, specifically building upon Lemma 2.This finding contributes to a deeper understanding of the relationship between a graphs structure and the properties of its eccentric graph.

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  1. Determination of all graphs whose eccentric graphs are clusters | Akiyama | Electronic Journal of Graph... doi.org/10.5614/ejgta.2024.12.2.1Determination of all graphs whose eccentric graphs are clusters Akiyama Electronic Journal of Graph doi 10 5614 ejgta 2024 12 2 1
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