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 graphs in terms of invariants of the factor graphs involvedin the product. As a consequence of the study, we show that theproblem offinding the super domination number of a graph is NP-Hard (16) (PDF) On the super domination number of lexicographic product graphs. Available from: https://www.researchgate.net/publication/315382754_On_the_super_domination_number_of_lexicographic_product_graphs [accessed Jul 28 2020].
Authors
- dr inż. Magda Dettlaff link open in new tab ,
- dr inż. Magdalena Lemańska link open in new tab ,
- Juan A. RODRíGUEZ-VELáZQUEZ,
- Rita Zuazua
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.1016/j.dam.2018.03.082
- Category
- Publikacja w czasopiśmie
- Type
- artykuły w czasopismach
- Language
- angielski
- Publication year
- 2019
