Abstract
The eccentricity e(υ) of vertex υ is defined as a distance to a farthest vertex from υ. The radius of a graph G is defined as r(G) = \( \mathop {\min }\limits_{u \in V(G)} \) {e(u)}. We consider properties of unchanging the radius of a graph under two different situations: deleting an arbitrary edge and deleting an arbitrary vertex. This paper gives the upper bounds for the number of edges in such graphs.
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(Communicated by Anatolij Dvurečenskij)
Supported by VEGA grant No. 1/0084/08.
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Vacek, O. The number of edges of radius-invariant graphs. Math. Slovaca 59, 201–220 (2009). https://doi.org/10.2478/s12175-009-0118-3
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DOI: https://doi.org/10.2478/s12175-009-0118-3