@article { author = {Imani, Elham and Mirzavaziri, Madjid}, title = {Self-Centered Graphs With Diameter 3}, journal = {Khayyam Journal of Mathematics}, volume = {8}, number = {1}, pages = {17-24}, year = {2022}, publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)}, issn = {2423-4788}, eissn = {2423-4788}, doi = {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, ‎and‎‎investigate 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}, url = {https://www.kjm-math.org/article_144156.html}, eprint = {https://www.kjm-math.org/article_144156_42059584a0f7906cadbfc57bede8fab3.pdf} }