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Roman domination in signed graphs
2022Summary: Let \(S = (G, \sigma)\) be a signed graph. A function \(f: V \rightarrow \{0,1,2\}\) is a Roman dominating function on \(S\) if (i) for each \(v \in V\), \(f(N[v]) = f(v) + \sum_{u \in N(v)} \sigma (uv) f(u) \geq 1\) and (ii) for each vertex \(v\) with \(f(v) = 0\) there exists a vertex \(u\in N^+(v)\) such that \(f(u) = 2\).
Joseph, James, JOSEPH, MAYAMMA
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Roman domination number of signed graphs
2022Summary: A function \(f:V \rightarrow \{0,1,2\}\) on a signed graph \(S=(G,\sigma)\) where \(G = (V,E)\) is a Roman dominating function (RDF) if \(f(N[v]) = f(v) + \sum_{u \in N(v)} \sigma (uv)f(u) \geq 1\) for all \(v\in V\) and for each vertex \(v\) with \(f(v)=0\) there is a vertex \(u\) in \(N^+(v)\) such that \(f(u) = 2\). The weight of an RDF \(f\
Joseph, James, JOSEPH, MAYAMMA
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The signed Roman domination number of two classes graphs
Discrete Mathematics, Algorithms and Applications, 2020Let [Formula: see text] be a simple graph with vertex set [Formula: see text] and edge set [Formula: see text]. A signed Roman dominating function (SRDF) of [Formula: see text] is a function [Formula: see text] satisfying the conditions that (i) [Formula: see text] for each [Formula: see text], where [Formula: see text] is the set, called closed ...
Xia Hong 0005 +3 more
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Signed double Roman domination numbers in digraphs
Annals of the University of Craiova - Mathematics and Computer Science Series, 2021"Let $D=(V,A)$ be a finite simple digraph. A signed double Roman dominating function (SDRD-function) on the digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2, 3\}$ satisfying the following conditions: (i) $\sum_{x\in N^-[v]}f(x)\ge 1$ for each $v\in V(D)$, where $N^-[v]$ consist of $v$ and all in-neighbors of $v$, and (ii) if $f(v)=-1$, then the ...
Jafar Amjadi, Fatemeh Pourhosseini
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Twin signed double Roman domination numbers in directed graphs
Discrete Mathematics, Algorithms and Applications, 2022Let [Formula: see text] be a finite simple directed graph (shortly digraph). A function [Formula: see text] is called a twin signed double Roman dominating function (TSDRDF) if (i) every vertex [Formula: see text] with [Formula: see text] has at least two in-neighbor assigned a 2 or at least an in-neighbor [Formula: see text] with [Formula: see text],
Akram Mahmoodi +2 more
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Bounds on the signed total Roman 2-domination in graphs
Discrete Mathematics, Algorithms and Applications, 2020Let [Formula: see text] be an integer and [Formula: see text] be a simple and finite graph with vertex set [Formula: see text]. A signed total Roman [Formula: see text]-dominating function (STR[Formula: see text]DF) on a graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text ...
R. Khoeilar +3 more
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Signed total double Roman k-domination in graphs
Discrete Mathematics, Algorithms and Applications, 2019A signed total double Roman [Formula: see text]-dominating function (STDRkDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text] has at least two neighbors assigned 2 under [Formula: see text] or at least one neighbor [Formula: see text] with [Formula:
L. Shahbazi +3 more
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Signed double Roman \(k\)-domination in graphs [PDF]
Australas. J Comb., 2018 Summary: Let \(G=(V,E)\) be a simple and finite graph with vertex set \(V(G)\), and let \(k\geq 1\) be an integer. A signed double Roman \(k\)-dominating function (SDR\(k\)DF) on a graph \(G\) is a function \(f:V(G)\rightarrow \{-1,1,2,3\}\) such that (i) every vertex \(v\) with \(f(v)=-1\) is adjacent to at least two vertices assigned with 2 or to at ...
Jafar Amjadi +4 more
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On the signed strong Roman domination number of graphs
Discrete Mathematics, Algorithms and Applications, 2020Let [Formula: see text] be a finite and simple graph of order [Formula: see text] and maximum degree [Formula: see text]. A signed strong Roman dominating function on a graph [Formula: see text] is a function [Formula: see text] satisfying the conditions that (i) for every vertex [Formula: see text] of [Formula: see text], [Formula: see text], where ...
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Bounds for signed double Roman k-domination in trees
RAIRO - Operations Research, 2019Let k ≥ 1 be an integer and G be a simple and finite graph with vertex set V(G). A signed double Roman k-dominating function (SDRkDF) on a graph G is a function f:V(G) → {−1,1,2,3} such that (i) every vertex v with f(v) = −1 is adjacent to at least two vertices assigned a 2 or to at least one vertex w with f(w) = 3, (ii) every vertex v with f(v) = 1 is
Hong Yang +6 more
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