On strong digraphs with a prescribed ultracenter

Authors: Chartrand G.¹; Gavlas H.¹; Schulz K.¹; Winters S.J.²

Source: Czechoslovak Mathematical Journal, Volume 47, Number 1, March 1997 , pp. 83-94(12)

Publisher: Springer

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Abstract:

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 radD and the subdigraph induced by the central vertices is the center C(D). For a central vertex v in a strong digraph D with radD < 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 uradD 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.

Language: English

Document Type: Research article

Affiliations: 1: Western Michigan University, Department of Mathematics and Statistics, Kalamazoo, Michigan 49008-5152, U.S.A. 2: University of Wiscousin Oshkosh, U.S.A.

Publication date: 1997-03-01