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2005 | 25 | 1-2 | 183-196
Tytuł artykułu

Median and quasi-median direct products of graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of G×P₃ is median if and only if G is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form G×K₂ are proved, and it is shown that the only nonbipartite quasi-median direct product is K₃×K₃.
Wydawca
Rocznik
Tom
25
Numer
1-2
Strony
183-196
Opis fizyczny
Daty
wydano
2005
otrzymano
2003-11-29
poprawiono
2004-09-01
Twórcy
  • University of Maribor, FEECS, Smetanova 17, 2000 Maribor, Slovenia
  • Department of Computer Science, St. Cloud State University, 720 Fourth Ave. S., St. Cloud, MN 56301, USA
  • Department of Mathematics and Computer Science, PEF, University of Maribor, Koroska 160, 2000 Maribor, Slovenia
autor
  • University of Maribor, FME, Smetanova 17, 2000 Maribor, Slovenia
Bibliografia
  • [1] G. Abay-Asmerom and R. Hammack, Centers of tensor products of graphs, Ars Combin., to appear.
  • [2] H.-J. Bandelt, Retracts of hypercubes, J. Graph Theory 8 (1984) 501-510, doi: 10.1002/jgt.3190080407.
  • [3] H.-J. Bandelt, G. Burosch and J.-M. Laborde, Cartesian products of trees and paths, J. Graph Theory 22 (1996) 347-356, doi: 10.1002/(SICI)1097-0118(199608)22:4<347::AID-JGT8>3.0.CO;2-L
  • [4] H.-J. Bandelt, H.M. Mulder and E. Wilkeit, Quasi-median graphs and algebras, J. Graph Theory 18 (1994) 681-703, doi: 10.1002/jgt.3190180705.
  • [5] B. Brešar, W. Imrich and S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory 23 (2003) 227-240, doi: 10.7151/dmgt.1199.
  • [6] B. Brešar, S. Klavžar and R. Skrekovski, Quasi-median graphs, their generalizations, and tree-like equalities, European J. Combin. 24 (2003) 557-572, doi: 10.1016/S0195-6698(03)00045-3.
  • [7] M. Deza and M. Laurent, Geometry of Cuts and Metrics (Springer-Verlag, Berlin, 1997).
  • [8] D. Djoković, Distance preserving subgraphs of hypercubes, J. Combin. Theory (B) 14 (1973) 263-267, doi: 10.1016/0095-8956(73)90010-5.
  • [9] J. Hagauer and S. Klavžar, Clique-gated graphs, Discrete Math. 161 (1996) 143-149, doi: 10.1016/0012-365X(95)00280-A.
  • [10] W. Imrich, Factoring cardinal product graphs in polynomial time, Discrete Math. 192 (1998) 119-144, doi: 10.1016/S0012-365X(98)00069-7.
  • [11] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (Wiley, New York, 2000).
  • [12] P.K. Jha, S. Klavžar and B. Zmazek, Isomorphic components of Kronecker products of bipartite graphs, Discuss. Math. Graph Theory 17 (1997) 301-309, doi: 10.7151/dmgt.1057.
  • [13] S.-R. Kim, Centers of a tensor composite graph, in: Proceedings of the Twenty-second Southeastern Conference on Combinatorics, Graph Theory, and Computing (Baton Rouge, LA, 1991), Congr. Numer. 81 (1991) 193-203.
  • [14] S. Klavžar and H.M. Mulder, Median graphs: characterizations, location theory and related structures, J. Combin. Math. Combin. Comp. 30 (1999) 103-127.
  • [15] S. Klavžar and R. Skrekovski, On median graphs and median grid graphs, Discrete Math. 219 (2000) 287-293, doi: 10.1016/S0012-365X(00)00085-6.
  • [16] H.M. Mulder, The structure of median graphs, Discrete Math. 24 (1978) 197-204, doi: 10.1016/0012-365X(78)90199-1.
  • [17] H.M. Mulder, The Interval Function of a Graph (Mathematisch Centrum, Amsterdam, 1980).
  • [18] C. Tardif, On compact median graphs, J. Graph Theory 23 (1996) 325-336, doi: 10.1002/(SICI)1097-0118(199612)23:4<325::AID-JGT1>3.0.CO;2-T
  • [19] P.M. Weichsel, The Kronecker product of graphs, Proc. Amer. Math. Soc. 13 (1962) 47-52, doi: 10.1090/S0002-9939-1962-0133816-6.
  • [20] P.M. Winkler, Isometric embedding in products of complete graphs, Discrete Appl. Math. 7 (1984) 221-225, doi: 10.1016/0166-218X(84)90069-6.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1271
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