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2000 | 20 | 2 | 271-280
Tytuł artykułu

Domination and independence subdivision numbers of graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The domination subdivision number $sd_γ(G)$ of a graph is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number. Arumugam showed that this number is at most three for any tree, and conjectured that the upper bound of three holds for any graph. Although we do not prove this interesting conjecture, we give an upper bound for the domination subdivision number for any graph G in terms of the minimum degrees of adjacent vertices in G. We then define the independence subdivision number $sd_β(G)$ to equal the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the independence number. We show that for any graph G of order n ≥ 2, either $G = K_{1,m}$ and $sd_β(G) = m$, or $1 ≤ sd_β(G) ≤ 2$. We also characterize the graphs G for which $sd_β(G) = 2$.
Słowa kluczowe
Wydawca
Rocznik
Tom
20
Numer
2
Strony
271-280
Opis fizyczny
Daty
wydano
2000
otrzymano
2000-08-04
Twórcy
  • Department of Mathematics, East Tennessee State University, Johnson City, TN 37614 USA
  • Department of Computer Science, Clemson University, Clemson, SC 29634 USA
  • Department of Computer Science, Clemson University, Clemson, SC 29634 USA
Bibliografia
  • [1] S. Arumugam, private communication, June 2000.
  • [2] C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam, 1973).
  • [3] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (American Elsevier, New York, 1977).
  • [4] G. Chartrand and L. Lesniak, Graphs & Digraphs (Wadsworth and Brooks/Cole, Monterey, CA, third edition, 1996).
  • [5] F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969).
  • [6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, 1998).
  • [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs, Advanced Topics (Marcel Dekker, Inc., New York, 1998).
  • [8] G. Hopkins and W. Staton, Graphs with unique maximum independent sets, Discrete Math. 57 (1985) 245-251, doi: 10.1016/0012-365X(85)90177-3.
  • [9] D.B. West, Introduction to Graph Theory (Prentice Hall, New Jersey, 1996).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1126
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