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2015 | 35 | 3 | 439-446
Tytuł artykułu

The Median Problem on k-Partite Graphs

Treść / Zawartość
Warianty tytułu
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
Wydawca
Rocznik
Tom
35
Numer
3
Strony
439-446
Opis fizyczny
Daty
wydano
2015-08-01
otrzymano
2014-02-24
poprawiono
2014-06-20
zaakceptowano
2014-08-15
online
2015-07-29
Twórcy
  • Cochin University of Science and Technology Cochin-682022 India, vambat@gmail.com
Bibliografia
  • [1] K. Balakrishnan, B. Brešar, M. Kovše, M. Changat, A.R. Subhamathi and S. Klavžar, Simultaneous embeddings of graphs as median and antimedian ubgraphs, Networks 56 (2010) 90-94. doi:10.002/net.20350[WoS]
  • [2] R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory, Second Edition (Heidelberg, Springer, 2012). doi:10.1007/978-1-4614-4529-6[Crossref]
  • [3] H. Bielak and M.M. Sys lo, Peripheral vertices in graphs, Studia Sci. Math. Hungar. 18 (1983) 269-275.
  • [4] H. Kautz, B. Selman and M. Shah, Referral Web: combining social networks and collaborative filtering, Communications of the ACM 40(3) (1997) 63-65. doi:10.1145/245108.245123[Crossref]
  • [5] K. Pravas and A. Vijayakumar, Convex median and anti-median at pre- scribed distance, communicated.
  • [6] P.J. Slater, Medians of arbitrary graphs, J. Graph Theory 4 (1980) 389-392. doi:10.1002/jgt.3190040408[Crossref]
  • [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.
  • [8] H.G. Yeh and G.J. Chang, Centers and medians of distance-hereditary graphs, Discrete Math. 265 (2003) 297-310. doi:10.1016/S0012-365X(02)00630-1 [Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1802
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