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2005 | 25 | 3 | 251-259
Tytuł artykułu

Domination and leaf density in graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The domination number γ(G) of a graph G is the minimum cardinality of a subset D of V(G) with the property that each vertex of V(G)-D is adjacent to at least one vertex of D. For a graph G with n vertices we define ε(G) to be the number of leaves in G minus the number of stems in G, and we define the leaf density ζ(G) to equal ε(G)/n. We prove that for any graph G with no isolated vertex, γ(G) ≤ n(1- ζ(G))/2 and we characterize the extremal graphs for this bound. Similar results are obtained for the total domination number and the partition domination number.
Wydawca
Rocznik
Tom
25
Numer
3
Strony
251-259
Opis fizyczny
Daty
wydano
2005
otrzymano
2003-05-19
poprawiono
2003-10-01
Twórcy
  • Department of Mathematics, Aalborg University, Fredrik Bajers Vej 7G, DK 9220 Aalborg, Denmark
Bibliografia
  • [1] R.C. Brigham, J.R. Carrington and R.P. Vitray, Connected graphs with maximum total domination number, J. Combin. Math. Combin. Comput. 34 (2000) 81-95.
  • [2] E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211-219, doi: 10.1002/net.3230100304.
  • [3] J.F. Fink, M.S. Jacobson, L.F. Kinch and J. Roberts, On graphs having domination number half their order, Period. Math. Hungar. 16 (1985) 287-293, doi: 10.1007/BF01848079.
  • [4] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness (Freeman, New York, 1979).
  • [5] B.L. Hartnell and P.D. Vestergaard, Partitions and domination in a graph, J. Combin. Math. Combin. Comput. 46 (2003) 113-128.
  • [6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs (Marcel Dekker, Inc., 1998).
  • [7] A.M. Henning and P.D. Vestergaard, Domination in partitioned graphs with minimum degree two (Manuscript, 2002).
  • [8] O. Ore, Theory of Graphs (Amer. Math. Soc. Colloq. Publ., 1962).
  • [9] C. Payan and N.H. Xuong, Domination-balanced graphs, J. Graph Theory 6 (1982) 23-32, doi: 10.1002/jgt.3190060104.
  • [10] S.M. Seager, Partition dominations of graphs of minimum degree 2, Congr. Numer. 132 (1998) 85-91.
  • [11] Z. Tuza and P.D. Vestergaard, Domination in partitioned graphs, Discuss. Math. Graph Theory 22 (2002) 199-210, doi: 10.7151/dmgt.1169.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1278
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