Czechoslovak Mathematical Journal
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Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library Surmnary. The (directed) distance from a vertex u to a vertex v in a strong digraph D is the length of a shortest u-v (directed) path in D. The eccentricity of a vertex v of D is the distance from v to a vertex furthest from v in D. The radius radD is the minimum eccentricity among the vertices of D and the diameter diamD is the maximum eccentricity. A central vertex is a vertex with eccentricity rad D and the subdigraph induced by the central vertices is the center C(D). For a central vertex v in a strong digraph D with rad D < diamD, the central distance c(v) of v is the greatest nonnegative integer n such that whenever d(v,x) ^ n, then x is in C(D). The maximum central distance among the central vertices of D is the ultraradius uradD and the subdigraph induced by the central vertices with central distance uraclD is the ultracenter UC(D). For a given digraph D, the problem of determining a strong digraph H with UC(H) = D and C(H) ?-D is studied. This problem is also considered for digraphs that are asymmetric.
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Czechoslovak Mathematical Journal
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تاریخ انتشار 2012