Results 11 to 20 of about 86,658 (242)
Dominating the Direct Product of Two Graphs through Total Roman Strategies [PDF]
Mathematics, 2020 Given a graph G without isolated vertices, a total Roman dominating function for G is a function f:V(G)→{0,1,2} such that every vertex u with f(u)=0 is adjacent to a vertex v with f(v)=2, and the set of vertices with positive labels induces a graph of ...
Abel Cabrera Martínez +3 more
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Computational Complexity of Outer-Independent Total and Total Roman Domination Numbers in Trees
IEEE Access, 2018 An outer-independent total dominating set (OITDS) of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent.
Zepeng Li +4 more
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An Upper Bound on the Total Roman { 2 } -domination Number of Graphs with Minimum Degree Two [PDF]
Journal of Combinatorial Mathematics and Combinatorial ComputingA total Roman \(\{2\}\)-dominating function on a graph \(G = (V,E)\) is a function \(f:V\rightarrow\{0,1,2\}\) with the properties that (i) for every vertex \({v}\in V\) with \(f({v})=0\), \(f(N({v}))\ge2\) and (ii) the set of vertices with \(f({v})>0\) induces a subgraph with no isolated vertices.
Kheibari, M. +3 more
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AKCE International Journal of Graphs and Combinatorics, 2022 H. Abdollahzadeh Ahangar
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Several Roman domination graph invariants on Kneser graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 This paper considers the following three Roman domination graph invariants on Kneser graphs: Roman domination, total Roman domination, and signed Roman domination.
Tatjana Zec, Milana Grbić
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Hop total Roman domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 In this article, we initiate a study of hop total Roman domination defined as follows: a hop total Roman dominating function (HTRDF) on a graph [Formula: see text] is a function [Formula: see text] such that for every vertex u with f(u) = 0 there exists ...
H. Abdollahzadeh Ahangar +3 more
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From Total Roman Domination in Lexicographic Product Graphs to Strongly Total Roman Domination in Graphs [PDF]
, 2021 [EN] Let G be a graph with no isolated vertex and let N (v) be the open neighbourhood of v is an element of V (G). Let f : V (G) -> {0, 1, 2} be a function and V-i = {v is an element of V (G) : f (v) = i} for every i is an element of{0, 1, 2}.
Almerich-Chulia, Ana +3 more
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Maximum Second Zagreb Index Of Trees With Given Roman Domination Number [PDF]
Transactions on Combinatorics, 2023 Chemical study regarding total $\pi$-electron energy with respect to conjugated molecules has focused on the second Zagreb index of graphs. Moreover, in the last half-century, it has gotten a lot of attention.
Ayu Ameliatul Ahmad Jamri +3 more
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Total double Roman domination in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:V\rightarrow\{0,1,2,3\}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one ...
Guoliang Hao +2 more
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Quasi-total Roman reinforcement in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 A quasi-total Roman dominating function (QTRD-function) on [Formula: see text] is a function [Formula: see text] such that (i) every vertex x for which f(x) = 0 is adjacent to at least one vertex v for which f(v) = 2, and (ii) if x is an isolated vertex ...
N. Ebrahimi +3 more
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