Radius-invariant graphs

summary:The eccentricity $e(v)$ of a vertex $v$ is defined as the distance to a farthest vertex from $v$. The radius of a graph $G$ is defined as a $r(G)=\min _{u \in V(G)}\lbrace e(u)\rbrace $. A graph $G$ is radius-edge-invariant if $r(G-e)=r(G)$ for every $e \in E(G)$, radius-vertex-invariant if $r(G-v)= r(G)$ for every $v \in V(G)$ and radius-adding-invariant if $r(G+e)=r(G)$ for every $e \in E(\overline{G})$. Such classes of graphs are studied in this paper