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Distance independence in graphs

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EN
Abstrakty
EN
For a set D of positive integers, we define a vertex set S ⊆ V(G) to be D-independent if u, v ∈ S implies the distance d(u,v) ∉ D. The D-independence number $β_D(G)$ is the maximum cardinality of a D-independent set. In particular, the independence number $β(G) = β_{{1}}(G)$. Along with general results we consider, in particular, the odd-independence number $β_{ODD}(G)$ where ODD = {1,3,5,...}.
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Twórcy
  • Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899 USA
  • Department of Mathematical Sciences and Computer Sciences Department, University of Alabama in Huntsville, Huntsville, AL 35899 USA
Bibliografia
  • [1] E.J. Cockayne, S.T. Hedetniemi, and D.J. Miller, Properties of hereditary hypergraphs and middle graphs, Canad. Math. Bull. 21 (1978) 461-468, doi: 10.4153/CMB-1978-079-5.
  • [2] T. Gallai, Über extreme Punkt-und Kantenmengen, Ann. Univ. Sci. Budapest, Eotvos Sect. Math. 2 (1959) 133-138.
  • [3] T.W. Haynes and P.J. Slater, Paired domination in graphs, Networks 32 (1998) 199-206, doi: 10.1002/(SICI)1097-0037(199810)32:3<199::AID-NET4>3.0.CO;2-F
  • [4] J.D. McFall and R. Nowakowski, Strong indepedence in graphs, Congr. Numer. 29 (1980) 639-656.
  • [5] J.L. Sewell, Distance Generalizations of Graphical Parameters, (Univ. Alabama in Huntsville, 2011).
  • [6] A. Sinko and P.J. Slater, Generalized graph parametric chains, submitted for publication.
  • [7] A. Sinko and P.J. Slater, R-parametric and R-chromatic problems, submitted for publication.
  • [8] P.J. Slater, Enclaveless sets and MK-systems, J. Res. Nat. Bur. Stan. 82 (1977) 197-202.
  • [9] P.J. Slater, Generalized graph parametric chains, in: Combinatorics, Graph Theory and Algorithms (New Issues Press, Western Michigan University 1999) 787-797.
  • [10] T.W. Haynes, M.A. Henning and P.J. Slater, Strong equality of upper domination and independence in trees, Util. Math. 59 (2001) 111-124.
  • [11] T.W. Haynes, M.A. Henning and P.J. Slater, Strong equality of domination parameters in trees, Discrete Math. 260 (2003) 77-87, doi: 10.1016/S0012-365X(02)00451-X.
  • [12] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, LP-duality, complementarity and generality of graphical subset problems, in: Domination in Graphs Advanced Topics, T.W. Haynes et al. (eds) (Marcel-Dekker, Inc. 1998) 1-30.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1554
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