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A Characterization of Trees With Equal Independent Domination and Secure Domination Numbers
Information Processing Letters, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zepeng Li
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Independent transversal domination number in complementary prisms
, 2021 Summary: A set \(D \subseteq V(G)\) is an independent transversal dominating set of \(G\) if \(D\) is a dominating set and also intersects every maximum independent set in \(G\). The minimum cardinality of such a set is equal to the transversal domination number, denoted by \(\gamma_\mathrm{it}(G)\).
Aytac, Aysun, Erkal, Cem
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2-Outer-Independent Domination in Graphs [PDF]
The National Academy of Sciences, India, 2015 We initiate the study of 2-outer-independent domination in graphs. A 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V (G) \D has at least two neighbors in D, and the set V (G)\D is independent. The 2-
Marcin Krzywkowski, Nader Jafari Rad
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Trees with independent Roman domination number twice the independent domination number
Discrete Mathematics, Algorithms and Applications, 2015A Roman dominating function (RDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula: see text] for which [Formula: see text] is adjacent to at least one vertex [Formula: see text] for which [Formula: see text].
Mustapha Chellali, Nader Jafari Rad
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On Domination and Independence Numbers of Graphs
Results in Mathematics, 1990The authors characterize those graphs which (1) have equal domination and independence numbers, and (2) are either bipartite or are block graphs, i.e., graphs in which every block is a complete graph.
Topp, Jerzy, Volkmann, Lutz
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Domination critical graphs with higher independent domination numbers
Journal of Graph Theory, 1996Let \(\gamma(G)\) be the domination number of a graph \(G\) and denote by \(i(G)\) its independent domination number. We say that a graph \(G\) is domination critical, if for every edge \(e\in \overline E(G)\), we have \(\gamma(G+ e)< \gamma(G)\). Obviously, \(\gamma(G)\leq i(G)\). It was conjectured that if \(G\) is a domination critical graph with \(\
S. Ao +3 more
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Cubic Graphs with Large Ratio of Independent Domination Number to Domination Number
Graphs and Combinatorics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Suil O, Douglas B. West
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The domination and independent domination numbers of some families of snarks
Ars Mathematica ContemporaneaIt is known that for an arbitrary graph \(G\), determining either its domination number \(\gamma(G)\) or independent domination number \(i(G)\) is an NP-hard problem. Therefore, establishing bounds for and determining these two domination parameters for particular classes of graphs (especially for cubic graphs) received much attention.
Alessandra A. Pereira +1 more
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Independent Domination Number of Planar Triangulations
Journal of Graph TheoryABSTRACTWe show that every planar triangulation on vertices has a maximal independent set of size at most . This affirms a conjecture by Botler, Fernandes, and Gutiérrez (Electron. J. Comb., 2024) based on an open question of Goddard and Henning (Appl. Math. Comput., 2020).
P. Francis +3 more
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