Centers in Inserted Graphs

L. K. Pramanik

In this paper we study some concepts involving distance in inserted graphs with an emphasize on centers in inserted graphs. More precisely we prove that for every non-trivial connected graph $H$ there exists a graph $G$ such that $H$ is the center of $G$ and the inserted graph of $H$ is the center of the inserted graph of $G$. Graphs which are the periphery of some inserted graph are characterized.