MATHEMATICA BOHEMICA, Vol. 129, No. 4, pp. 361-377 (2004)

Radius-invariant graphs

V. Balint, O. Vacek

V. Balint, Department of Numerical and Optimization Methods, Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48 Bratislava, Slovak Republic, e-mail; O. Vacek, Department of Mathematics and Descriptive Geometry, Faculty of Wooden Science, Technical University Zvolen, T. G. Masaryka 24, 960 53 Zvolen, Slovak Republic, e-mail

Abstract: 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 $r(G)=\min_{u \in V(G)}\{ e(u)\}$. 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.

Keywords: radius of graph, radius-invariant graphs

Classification (MSC2000): 05C12, 05C35, 05C75

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