Wyniki wyszukiwania dla: LEXICOGRAPHIC PRODUCT

• On the super domination number of lexicographic product graphs

  Publikacja

  • M. Dettlaff
  • M. Lemańska
  • J. A. RODRíGUEZ-VELáZQUEZ
  • R. Zuazua

  - DISCRETE APPLIED MATHEMATICS - Rok 2019

  The neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product...

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• Mobile mutual-visibility sets in graphs

  Publikacja

  • M. Lemańska
  • M. Dettlaff
  • J. A. Rodriguez-Velazquez
  • I. G. Yero

  - ARS Mathematica Contemporanea - Rok 2025

  Given a connected graph G, the mutual-visibility number of G is the cardinality of a largest set S such that for every pair of vertices x, y ∈ S there exists a shortest x, y-path whose interior vertices are not contained in S. Assume that a robot is assigned to each vertex of the set S. At each stage, one robot can move to a neighbouring vertex. Then S is a mobile mutual-visibility set of G if there exists a sequence of moves of...

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