Results 31 to 40 of about 152,920 (311)
Progress on Roman and Weakly Connected Roman Graphs
Mathematics, 2021 A graph G for which γR(G)=2γ(G) is the Roman graph, and if γRwc(G)=2γwc(G), then G is the weakly connected Roman graph. In this paper, we show that the decision problem of whether a bipartite graph is Roman is a co-NP-hard problem. Next, we prove similar
Joanna Raczek, Rita Zuazua
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Maximal first Zagreb index of trees with given Roman domination number
AIMS Mathematics, 2022 The first Zagreb index of graphs is defined to be the sum of squares of degrees of all the vertices of graphs. It drew a great deal of attention in the past half-century.
Z. Du +3 more
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On trees with equal Roman domination and outer-independent Roman domination numbers
Communications in Combinatorics and Optimization, 2019 Summary: 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 \(f(v) = 2\). A Roman dominating function \(f\) is called an outer-independent Roman dominating function (OIRDF) on \(G\) if ...
Sheikholeslami, Seyed Mahmoud +1 more
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The Roman domination number of some special classes of graphs - convex polytopes
Applicable Analysis and Discrete Mathematics, 2021 In this paper we study the Roman domination number of some classes of planar graphs - convex polytopes: An, Rn and Tn. We establish the exact values of Roman domination number for: An, R3k, R3k+1, T8k, T8k+2, T8k+3, T8k+5 and T8k+6.
Aleksandar Kartelj +3 more
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A characterization of trees with equal Roman 2-domination and Roman domination numbers
Communications in Combinatorics and Optimization, 2019 Summary: Given a graph \(G=(V,E)\) and a vertex \(v \in V\), by \(N(v)\) we represent the open neighbourhood of \(v\). Let \(f:V\rightarrow \{0,1,2\}\) be a function on \(G\). The weight of \(f\) is \(\omega(f)=\sum_{v\in V}f(v)\) and let \(V_i=\{v\in V :f(v)=i\}\), for \(i=0,1,2\).
Gonzalez Yero, Ismael +1 more
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Closed formulas for the total Roman domination number of lexicographic product graphs
Ars Math. Contemp., 2021 Let G be a graph with no isolated vertex and f : V ( G ) → {0, 1, 2} a function. Let V i = { x ∈ V ( G ) : f ( x ) = i } for every i ∈ {0, 1, 2} . We say that f is a total Roman dominating function on G if every vertex in V 0 is adjacent to at least
Abel Cabrera Martínez +1 more
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Coloring, location and domination of corona graphs [PDF]
, 2012 A vertex coloring of a graph $G$ is an assignment of colors to the vertices of $G$ such that every two adjacent vertices of $G$ have different colors. A coloring related property of a graphs is also an assignment of colors or labels to the vertices of a ...
Aguilar, A. Rondón +2 more
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Strong equality between the Roman domination and independent Roman domination numbers in trees
Discussiones Mathematicae Graph Theory, 2013 A Roman dominating function (RDF) 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 at least one vertex v for which f(v) = 2. The weight of an RDF is the value f(V (G)) = P u2V (G) f(u). An RDF f in a graph G is independent if no two vertices assigned positive values are
Chellali Mustapha, Rad Nader Jafari
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Bounds on the Total Double Roman Domination Number of Graphs
Discussiones Mathematicae Graph Theory, 2021 Let G be a simple graph with no isolated vertex and let γtdR(G) be the total double Roman domination number of G. In this paper, we present lower and upper bounds on γtdR (G) of a graph G in terms of the order, open packing number and the numbers of ...
Guoliang Hao +3 more
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Double Roman domination and domatic numbers of graphs
Communications in Combinatorics and Optimization, 2018 A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in \cite{bhh} as a function $f:V(G)\rightarrow\{0,1,2,3\}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least two neighbors assigned 2 ...
L. Volkmann
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