Self-Centered Graphs With Diameter 3

Document Type : Original Article

Authors

Elham Imani

Madjid Mirzavaziri

Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P. O. Box 1159, Mashhad 91775, Iran.

10.22034/kjm.2021.238888.1917

Abstract

‎A graph is called $3$-self-centered if all of its vertices have eccentricity $3.$ In this paper‎,
‎we study some properties of the $3$-self-centered graphs‎, ‎and‎
‎investigate the $3$-self-centered graphs with girth six or seven‎. ‎We determine‎
‎the vertex connectivity and regularity‎
‎of such graphs‎. ‎Moreover‎, ‎we show that if $G$ is a $3$-self-centered graph with girth seven‎, ‎then‎
‎$G$ is regular‎.

Keywords

Self-centered graph

Diameter

Girth

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