## Radius-invariant graphs.(English)Zbl 1080.05505

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 $$r(G)=\min _{u \in V(G)}\{ e(u)\}$$. 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.

### MSC:

 05C12 Distance in graphs 05C35 Extremal problems in graph theory 05C75 Structural characterization of families of graphs