Wyniki wyszukiwania dla: domination-related parameters

• Domination-Related Parameters in Rooted Product Graphs

  Publikacja

  • D. Kuziak
  • M. Lemańska
  • I. G. Yero

  - Bulletin of the Malaysian Mathematical Sciences Society - Rok 2016

  Abstract A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is adjacent to at least one vertex belonging to S. A domination parameter of G is related to those sets of vertices of a graph satisfying some domination property together with other conditions on the vertices of G. Here, we investigate several domination-related parameters in rooted product graphs.

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• Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs

  Publikacja

  • M. Dettlaff
  • J. Raczek
  • I. G. Yero

  - Opuscula Mathematica - Rok 2016

  Given a graph G= (V, E), the subdivision of an edge e=uv∈E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions...

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• Interpolation properties of domination parameters of a graph

  Publikacja

  • D. Kuziak

  - Australasian Journal of Combinatorics - Rok 2010

  An integer-valued graph function π is an interpolating function if a set π(T(G))={π(T): T∈TT(G)} consists of consecutive integers, where TT(G) is the set of all spanning trees of a connected graph G. We consider the interpolation properties of domination related parameters.

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• Relations between the domination parameters and the chromatic index of a graph

  Publikacja

  • W. Ulatowski

  - Discussiones Mathematicae Graph Theory - Rok 2009

  In this paper we show bounds for the sum and the product of the domination parameters and the chromatic index of a graph. We alsopresent some families of graphs for which these bounds are achieved.

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• Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number

  Publikacja

  • S. Bermudo
  • M. Dettlaff
  • M. Lemańska

  - DISCRETE APPLIED MATHEMATICS - Rok 2021

  Given two types of graph theoretical parameters ρ and σ, we say that a graph G is (σ, ρ)- perfect if σ(H) = ρ(H) for every non-trivial connected induced subgraph H of G. In this work we characterize (γw, τ )-perfect graphs, (γw, α′)-perfect graphs, and (α′, τ )-perfect graphs, where γw(G), τ (G) and α′(G) denote the weakly connected domination number, the vertex cover number and the matching number of G, respectively. Moreover,...

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• Changes in selected parameters related to proteolysis during ageing of dry-cured pork loins inoculated with probiotics

  Publikacja

  • J. Stadnik
  • Z. Dolatowski

  - Food Chemistry - Rok 2013

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• Domination subdivision and domination multisubdivision numbers of graphs

  Publikacja

  • M. Dettlaff
  • J. Raczek
  • J. Topp

  - Discussiones Mathematicae Graph Theory - Rok 2019

  The domination subdivision number sd(G) of a graph G 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 of G. It has been shown [10] that sd(T)<=3 for any tree T. We prove that the decision problem of the domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the domination multisubdivision number...

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• Graphs with equal domination and certified domination numbers

  Publikacja

  • M. Dettlaff
  • M. Lemańska
  • J. Topp
  • M. Miotk
  • R. Ziemann
  • P. Żyliński

  - Opuscula Mathematica - Rok 2019

  A setDof vertices of a graphG= (VG,EG) is a dominating set ofGif every vertexinVG−Dis adjacent to at least one vertex inD. The domination number (upper dominationnumber, respectively) ofG, denoted byγ(G) (Γ(G), respectively), is the cardinality ofa smallest (largest minimal, respectively) dominating set ofG. A subsetD⊆VGis calleda certified dominating set ofGifDis a dominating set ofGand every vertex inDhas eitherzero...

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• Certified domination

  Publikacja

  • M. Dettlaff
  • M. Lemańska
  • J. Topp
  • R. Ziemann
  • P. Żyliński

  - AKCE International Journal of Graphs and Combinatorics - Rok 2020

  Imagine that we are given a set D of officials and a set W of civils. For each civil x ∈ W, there must be an official v ∈ D that can serve x, and whenever any such v is serving x, there must also be another civil w ∈ W that observes v, that is, w may act as a kind of witness, to avoid any abuse from v. What is the minimum number of officials to guarantee such a service, assuming a given social network? In this paper, we introduce...

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• On trees with equal domination and total outer-independent domination numbers

  Publikacja

  • M. Krzywkowski

  - UTILITAS MATHEMATICA - Rok 2015

  For a graph G=(V,E), a subset D subseteq V(G) is a dominating set if every vertex of V(G)D has a neighbor in D, while it is a total outer-independent dominating set if every vertex of G has a neighbor in D, and the set V(G)D is independent. The domination (total outer-independent domination, respectively) number of G is the minimum cardinality of a dominating (total outer-independent dominating, respectively) set of G. We characterize...