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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Kodate, Takako
Tokyo Woman's Christian University
Electrical & Electronics Engineering

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Determination of all graphs whose eccentric graphs are clusters Akiyama, Jin; Kodate, Takako; Matsunaga, Kiyoko
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.2.1

Abstract

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].  
Co-Authors Akiyama, Jin Matsunaga, Kiyoko