Determination of all graphs whose eccentric graphs are clusters - Akiyama, Jin; Kodate, Takako; Matsunaga, Kiyoko (Electronic Journal of Graph Theory and Applications (EJGTA), 2024)
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].