Self-Centered Graphs With Diameter 3

Document Type : Original Article

Authors

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