The Median Problem on k-Partite Graphs

• Autorzy: Karuvachery Pravas , Ambat Vijayakumar
• Języki publikacji: EN

Abstrakty

EN

In a connected graph G, the status of a vertex is the sum of the distances of that vertex to each of the other vertices in G. The subgraph induced by the vertices of minimum (maximum) status in G is called the median (anti-median) of G. The median problem of graphs is closely related to the optimization problems involving the placement of network servers, the core of the entire networks. Bipartite graphs play a significant role in designing very large interconnection networks. In this paper, we answer a problem on the structure of medians of bipartite graphs by showing that any bipartite graph is the median (or anti-median) of another bipartite graph. Also, with a different construction, we show that the similar results hold for k-partite graphs, k ≥ 3. In addition, we provide constructions to embed another graph as center in both bipartite and k-partite cases. Since any graph is a k-partite graph, for some k, these constructions can be applied in general

Słowa kluczowe

EN

networks; distance; median; bipartite; k-partite.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 3
• Strony: 439-446

Daty

wydano

2015-08-01

otrzymano

2014-02-24

poprawiono

2014-06-20

zaakceptowano

2014-08-15

online

2015-07-29

Twórcy

autor

Karuvachery Pravas

• Government Polytechnic College Koratty-680 308 India

autor

Ambat Vijayakumar

• Cochin University of Science and Technology Cochin-682022 India

Bibliografia

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• [7] S.B. Rao and A.Vijayakumar, On the median and the anti-median of a co- graph, Int. J. Pure Appl. Math. 46 (2008) 703-710.
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Identyfikatory

DOI

10.7151/dmgt.1802