Geodesic
Radius-invariant graphs
Mathematica Bohemica, Tome 129 (2004) no. 4, pp. 361-377

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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.
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.
DOI : 10.21136/MB.2004.134047
Classification : 05C12, 05C35, 05C75
Keywords: radius of graph; radius-invariant graphs 
Bálint, V.; Vacek, O. Radius-invariant graphs. Mathematica Bohemica, Tome 129 (2004) no. 4, pp. 361-377. doi: 10.21136/MB.2004.134047
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