Results 11 to 20 of about 7,428 (262)
Isolate and independent domination number of some classes of graphs
AKCE International Journal of Graphs and Combinatorics, 2019 In this paper we compute isolate domination number and independent domination number of some well known classes of graphs. Also a counter example is provided, which disprove the result on independent domination for Euler Totient Cayley graph proved by ...
Shilpa T. Bhangale, Madhukar M. Pawar
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On trees with equal Roman domination and outer-independent Roman domination number [PDF]
Communications in Combinatorics and Optimization, 2019 A Roman dominating function (RDF) on a graph $G$ is a function $f : V (G) \to \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$.
S. Nazari-Moghaddam, S.M. Sheikholeslami
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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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An Improved Nordhaus–Gaddum-Type Theorem for 2-Rainbow Independent Domination Number
Mathematics, 2021 For a graph G, its k-rainbow independent domination number, written as γrik(G), is defined as the cardinality of a minimum set consisting of k vertex-disjoint independent sets V1,V2,…,Vk such that every vertex in V0=V(G)\(∪i=1kVi) has a neighbor in Vi ...
Enqiang Zhu
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Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs [PDF]
Opuscula Mathematica, 2016 Given a graph \(G=(V,E)\), the subdivision of an edge \(e=uv\in E(G)\) means the substitution of the edge \(e\) by a vertex \(x\) and the new edges \(ux\) and \(xv\).
Magda Dettlaff +2 more
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Distance-2 Independent Domination Numbers
DEStech Transactions on Computer Science and Engineering, 2017 The distance d(u,v) between two vertices u and v in a graph G equals the length of a shortest path from u to v. A distance-2 independent set of a graph G is a subset I of the vertices such that the distance between any two vertices of I in G is at least three.
Min-Jen JOU +3 more
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Independent Rainbow Domination Numbers of Generalized Petersen Graphs P(n,2) and P(n,3)
Mathematics, 2020 We obtain new results on independent 2- and 3-rainbow domination numbers of generalized Petersen graphs P ( n , k ) for certain values of n , k ∈ N . By suitably adjusting and applying a well established technique of tropical algebra (path
Boštjan Gabrovšek +2 more
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On independent domination numbers of grid and toroidal grid directed graphs [PDF]
Communications in Combinatorics and Optimization, 2019 A subset $S$ of vertex set $V(D)$ is an independent dominating set of a digraph $D$ if $S$ is both an independent and a dominating set of $D$. The independent domination number $i(D)$ is the minimum cardinality of an independent dominating set of $D ...
R. Shaheen
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An improved upper bound on the independent double Roman domination number of trees
AKCE International Journal of Graphs and Combinatorics, 2022 For a graph [Formula: see text] an independent double Roman dominating function (IDRDF) is a function [Formula: see text] having the property that: (i) every vertex [Formula: see text] with f(v) = 0 has a neighbor u with f(u) = 3 or at least two ...
F. Nahani Pour +3 more
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Independent partial domination
Cubo, 2021 For $p\in(0,1]$, a set $S\subseteq V$ is said to $p$-dominate or partially dominate a graph $G = (V, E)$ if $\frac{|N[S]|}{|V|}\geq p$. The minimum cardinality among all $p$-dominating sets is called the $p$-domination number and it is denoted by ...
L. Philo Nithya +1 more
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