Results 261 to 270 of about 10,563,621 (305)

Trees with Equal Domination and Restrained Domination Numbers

Journal of Global Optimization, 2006
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Dankelmann, Peter, Hattingh, Johannes H., Henning, Michael A., Swart, Henda C.   +3 more
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Note on the perfect Roman domination number of graphs

Applied Mathematics and Computation, 2020
In this note, we list some propositions of the perfect Roman domination number of graphs and give the characterization of graphs G with special value of the perfect Roman domination. Furthermore, γ R p ( F ) + γ R p ( F ¯ ) is given.
Jun Yue, Jiamei Song
semanticscholar   +1 more source

Split domination number of divisible dominating graphs

Journal of Discrete Mathematical Sciences and Cryptography, 2020
A graph G is a divisible dominating graph if the vertices are labeled with positive integers d and n except 0, such that the vertex labeled with n is adjacent to the vertex named with d if and only...
S. Amutha, K. Suriya Prabha, N. Anbazhagan, P. Shanthi   +3 more
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On trees with domination number equal to edge-vertex roman domination number

Discrete Mathematics, Algorithms and Applications, 2020
An edge-vertex Roman dominating function (or just ev-RDF) of a graph [Formula: see text] is a function [Formula: see text] such that for each vertex [Formula: see text] either [Formula: see text] where [Formula: see text] is incident with [Formula: see text] or there exists an edge [Formula: see text] adjacent to [Formula: see text] such that [Formula:
Naresh Kumar, H., Venkatakrishnan, Y. B.
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The Sierpiński domination number

Ars Mathematica Contemporanea
Let $G$ and $H$ be graphs and let $f \colon V(G)\rightarrow V(H)$ be a function. The Sierpiński product of $G$ and $H$ with respect to $f$, denoted by $G \otimes _f H$, is defined as the graph on the vertex set $V(G)\times V(H)$, consisting of $|V(G)|$ copies of $H$; for every edge $gg'$ of $G$ there is an edge between copies $gH$ and $g'H$ of $H ...
Henning, Michael A., Klavžar, Sandi, Kleszcz, Elżbieta, Pilśniak, Monika   +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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O, Suil, West, Douglas B.
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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].
Chellali, Mustapha, Rad, Nader Jafari
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Trees with equal Roman {2}-domination number and independent Roman {2}-domination number

RAIRO - Operations Research, 2019
A Roman {2}-dominating function (R{2}DF) on a graph G =(V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to either at least one vertex v with f(v) = 2 or two vertices v1, v2 with f(v1) = f(v2) = 1. The weight of an R{2}DF f is the value w(f) = ∑u∈Vf(u).
Pu Wu, Zepeng Li, Zehui Shao, Seyed Mahmoud Sheikholeslami   +3 more
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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 \(\
Ao, S., Cockayne, E. J., MacGillivray, G., Mynhardt, C. M.   +3 more
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New bounds on the double domination number of trees

Discrete Applied Mathematics, 2022
A. Cabrera-Martínez
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