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5 papers · 2 filters
From Italian domination in lexicographic product graphs to w-domination in graphs
A. Cabrera Martinez, A. Estrada-Moreno, J. A. Rodriguez-Velazquez
In this paper, we show that the Italian domination number of every lexicographic product graph can be expressed in terms of five different domination parameters of .…
Double domination in lexicographic product graphs
A. Cabrera Martinez, S. Cabrera Garcia, J. A. Rodriguez-Velazquez
In a graph , a vertex dominates itself and its neighbours. A subset is said to be a double dominating set of if dominates every vertex of at least…
Protection of graphs with emphasis on Cartesian product graphs
Magdalena Valveny, Juan Alberto Rodriguez-Velazquez
In this paper we study the weak Roman domination number and the secure domination number of a graph. In particular, we obtain general bounds on these two parameters and, as a conse…
Italian domination in rooted product graphs
R. Hernandez-Ortiz, L. P. Montejano, J. A. Rodriguez-Velazquez
In this article, we obtain closed formulae for the Italian domination number of rooted product graphs. As a particular case of the study, we derive the corresponding formulas for c…
Common Information, Matroid Representation, and Secret Sharing for Matroid Ports
Michael Bamiloshin, Aner Ben-Efraim, Oriol Farràs +1
Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have b…