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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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Some Results on the Strong Roman Domination Number of Graphs [PDF]
Mathematics Interdisciplinary Research, 2020 Let G=(V,E) be a finite and simple graph of order n and maximum degree Δ(G). A strong Roman dominating function on a graph G is a function f:V (G)→{0, 1,… ,[Δ(G)/2 ]+ 1} satisfying the condition that every vertex v for which f(v)=0 is
Akram Mahmoodi +2 more
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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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On [k]-Roman domination subdivision number of graphs
AKCE International Journal of Graphs and Combinatorics, 2022 Let [Formula: see text] be an integer and G a simple graph with vertex set V(G). Let f be a function that assigns labels from the set [Formula: see text] to the vertices of G.
K. Haghparast +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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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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Total Roman domination subdivision number in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$.
Jafar Amjad
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On a Relation between the Perfect Roman Domination and Perfect Domination Numbers of a Tree
Mathematics, 2020 A dominating set in a graph G is a set of vertices S ⊆ V ( G ) such that any vertex of V − S is adjacent to at least one vertex of S .
Zehui Shao +4 more
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Triple Roman domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2022 For a graph $G=(V, E)$, a triple Roman domination function is a function $f: V(G)\longrightarrow\{0, 1, 2, 3, 4\}$ having the property that for any vertex $v\in V(G)$, if $f(v)
Jafar Amjadi, Hakimeh Sadeghi
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A note on the Roman domatic number of a digraph [PDF]
Communications in Combinatorics and Optimization, 2020 A {\em Roman dominating function} on a digraph $D$ with vertex set $V(D)$ is a labeling $f\colon V(D)\to \{0, 1, 2\}$ such that every vertex with label $0$ has an in-neighbor with label $2$. A set $\{f_1,f_2,\ldots,f_d\}$ of Roman dominating functions
Lutz Volkmann, D. Meierling
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