Name
Abstract | ||
|---|---|---|
The directed distance d(D)(u, upsilon) from a vertex u to a vertex upsilon in a strong digraph D is the length of a shortest (directed) u - upsilon path in D. The eccentricity of a vertex upsilon in D is the directed distance from upsilon to a vertex furthest from upsilon. The distance of a vertex upsilon in D is the sum of the directed distances from upsilon to the vertices of D. The center C(D) of D is the subdigraph induced by those vertices of minimum eccentricity, while the median M(D) of D is the subdigraph induced by those vertices of minimum distance. It is shown that for every two asymmetric digraphs D1 and D2, there exists a strong asymmetric digraph H such that C(H) congruent-to D1 and M(H) congruent-to D2, and where the directed distance from C(H) to M(H) and from M(H) to C(H) can be arbitrarily prescribed. Furthermore, if K is a nonempty asymmetric digraph isomorphic to an induced subdigraph of both D1 and D2, then there exists a strong asymmetric digraph F such that C(F) congruent-to D1, M(F) congruent-to D2, and C(F) and M(F) congruent-to K. (C) 1993 John Wiley & Sons, Inc. |
Year | DOI | Venue |
|---|---|---|
1993 | 10.1002/jgt.3190170408 | Journal of Graph Theory |
Field | DocType | Volume |
Discrete mathematics,Topology,Combinatorics,Vertex (geometry),Graph isomorphism,Eccentricity (behavior),Directed graph,Isomorphism,Digraph,Mathematics | Journal | 17 |
Issue | ISSN | Citations |
4 | 0364-9024 | 5 |
PageRank | References | Authors |
0.59 | 1 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gary Chartrand | 1 | 5 | 0.93 |
| Garry L. Johns | 2 | 68 | 11.78 |
| Songlin Tian | 3 | 19 | 3.51 |
| Steven J. Winters | 4 | 12 | 6.33 |