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2005 | 25 | 3 | 391-406
Tytuł artykułu

An upper bound of the basis number of the strong product of graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The basis number of a graph G is defined to be the least integer d such that there is a basis B of the cycle space of G such that each edge of G is contained in at most d members of B. In this paper we give an upper bound of the basis number of the strong product of a graph with a bipartite graph and we show that this upper bound is the best possible.
Słowa kluczowe
Wydawca
Rocznik
Tom
25
Numer
3
Strony
391-406
Opis fizyczny
Daty
wydano
2005
otrzymano
2004-06-29
poprawiono
2005-01-03
Twórcy
  • Department of Mathematics, Yarmouk University, Irbid-Jordan
Bibliografia
  • [1] A.A. Ali, The basis number of complete multipartite graphs, Ars Combin. 28 (1989) 41-49.
  • [2] A.A. Ali and G.T. Marougi, The basis number of the strong product of graphs, Mu'tah Lil-Buhooth Wa Al-Dirasat 7 (1) (1992) 211-222.
  • [3] A.A. Ali and G.T. Marougi, The basis number of cartesian product of some graphs, J. Indian Math. Soc. 58 (1992) 123-134.
  • [4] A.S. Alsardary, An upper bound on the basis number of the powers of the complete graphs, Czechoslovak Math. J. 51 (126) (2001) 231-238, doi: 10.1023/A:1013734628017.
  • [5] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (America Elsevier Publishing Co. Inc., New York, 1976).
  • [6] R. Diestel, Graph Theory, Graduate Texts in Mathematics, 173 (Springer-Verlag, New York, 1997).
  • [7] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (Wiley, New York, 2000).
  • [8] W. Imrich and P. Stadler, Minimum cycle bases of product graphs, Australas. J. Combin. 26 (2002) 233-244.
  • [9] M.M.M. Jaradat, On the basis number of the direct product of graphs, Australas. J. Combin. 27 (2003) 293-306.
  • [10] M.M.M. Jaradat, The basis number of the direct product of a theta graph and a path, Ars Combin. 75 (2005) 105-111.
  • [11] P.K. Jha, Hamiltonian decompositions of product of cycles, Indian J. Pure Appl. Math. 23 (1992) 723-729.
  • [12] P.K. Jha and G. Slutzki, A note on outerplanarity of product graphs, Zastos. Mat. 21 (1993) 537-544.
  • [13] S. MacLane, A combinatorial condition for planar graphs, Fundamenta Math. 28 (1937) 22-32.
  • [14] G. Sabidussi, Graph multiplication, Math. Z. 72 (1960) 446-457, doi: 10.1007/BF01162967.
  • [15] E.F. Schmeichel, The basis number of a graph, J. Combin. Theory (B) 30 (1981) 123-129, doi: 10.1016/0095-8956(81)90057-5.
  • [16] P.M. Weichsel, The Kronecker product of graphs, Proc. Amer. Math. Soc. 13 (1962) 47-52, doi: 10.1090/S0002-9939-1962-0133816-6.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1291
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