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2-Outer-Independent Domination in Graphs

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-
Nader Jafari Rad, Marcin Krzywkowski, Krzywkowski Marcin   +2 more
exaly   +2 more sources

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Trees with independent Roman domination number twice the independent domination number

Discrete Mathematics, Algorithms and Applications, 2015
A 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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Perfect graphs of strong domination and independent strong domination

Discrete Mathematics, 2001
Let γ(G), i(G), γS(G) and iS(G) denote the domination number, the independent domination number, the strong domination number and the independent strong domination number of a graph G, respectively.
Dieter Rautenbach
exaly   +2 more sources

On Domination and Independence Numbers of Graphs

Results in Mathematics, 1990
The 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, 1996
Let \(\gamma(G)\) 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, Ernest J. Cockayne, Gary MacGillivray, Christina M. Mynhardt   +3 more
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Cubic Graphs with Large Ratio of Independent Domination Number to Domination Number

Graphs and Combinatorics, 2015
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Suil O, Douglas B. West
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The domination and independent domination numbers of some families of snarks

Ars Mathematica Contemporanea
It 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, Christiane Neme Campos   +1 more
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Independent Domination Number of Planar Triangulations

Journal of Graph Theory
ABSTRACTWe 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, Abraham M. Illickan, Lijo M. Jose, Deepak Rajendraprasad   +3 more
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On the Independent Domination Number of Random Regular Graphs

Combinatorics, Probability and Computing, 2006
A dominating set $\cal D$ of a graph $G$ is a subset of $V(G)$ such that, for every vertex $v\in V(G)$, either in $v\in {\cal D}$ or there exists a vertex $u \in {\cal D}$ that is adjacent to $v$. We are interested in finding dominating sets of small cardinality. A dominating set $\cal I$ of a graph $G$ is said to be independent if no two vertices of ${
William Duckworth, Nicholas C. Wormald
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Domination number, independent domination number and k-independence number in trees

Discrete Applied Mathematics
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Qing Cui, Xu Zou
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