3-SELF-CENTERED GRAPHS WITH GIRTH SIX OR SEVEN

A graph is called 3-self-centered if all of its vertices have the same eccentricity and equals to 3: In this paper, we investigated the 3-self-centered graphs with girth six or seven. We determined vertex connectivity and reg- ularity of graphs with above characteristics. Finally, we characterize all 3- self-centered graphs of order n with girth six such that number of edges is minimum.