Algorithmic aspects of Roman domination in graphs
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Applied Mathematics and Computing"
DOI: 10.1007/s12190-020-01345-4
Abstract: For a simple, undirected graph $$G = (V, E)$$ G = ( V , E ) , a Roman dominating function (RDF) $$f{:}V \rightarrow \lbrace 0, 1, 2 \rbrace $$ f : V → {… read more here.
Keywords: convex bipartite; graphs; bipartite graphs; roman domination ... See more keywords
Double Roman Domination in Digraphs
Sign Up to like & getrecommendations! Published in 2017 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-017-0582-9
Abstract: Let D be a finite and simple digraph with vertex set V(D). A double Roman dominating function (DRDF) on a digraph D is a function $$f:V(D)\rightarrow \{0,1,2,3\}$$f:V(D)→{0,1,2,3} satisfying the condition that if $$f(v)=0$$f(v)=0, then the… read more here.
Keywords: domination number; double roman; roman domination; domination ... See more keywords
Total Roman {2}-domination in graphs
Sign Up to like & getrecommendations! Published in 2019 at "Quaestiones Mathematicae"
DOI: 10.2989/16073606.2019.1695230
Abstract: Abstract Given a graph G = (V, E), a function f: V → {0, 1, 2} is a total Roman {2}-dominating function if every vertex ʋ ∈ V for which f (ʋ) = 0 satisfies… read more here.
Keywords: function; roman domination; domination; total roman ... See more keywords
Independent Roman Domination: The Complexity and Linear-Time Algorithm for Trees
Sign Up to like & getrecommendations! Published in 2022 at "Symmetry"
DOI: 10.3390/sym14020404
Abstract: For a graph G=(V,E), an independent Roman dominating function (IRDF) is a function f:V→{0,1,2} having the property that: (1) every vertex assigned a value of 0 is adjacent to at least one vertex assigned a… read more here.
Keywords: function; time algorithm; independent roman; linear time ... See more keywords
[k]-Roman Domination in Digraphs
Sign Up to like & getrecommendations! Published in 2023 at "Symmetry"
DOI: 10.3390/sym15030743
Abstract: Let D=(V(D),A(D)) be a finite, simple digraph and k a positive integer. A function f:V(D)→{0,1,2,…,k+1} is called a [k]-Roman dominating function (for short, [k]-RDF) if f(AN−[v])≥|AN−(v)|+k for any vertex v∈V(D), where AN−(v)={u∈N−(v):f(u)≥1} and AN−[v]=AN−(v)∪{v}. The… read more here.
Keywords: domination number; domination digraphs; domination; roman domination ... See more keywords
Signed strong Roman domination in graphs
Sign Up to like & getrecommendations! Published in 2017 at "Tamkang Journal of Mathematics"
DOI: 10.5556/j.tkjm.48.2017.2240
Abstract: Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximum degree $\Delta$. A signed strong Roman dominating function (abbreviated SStRDF) on a graph $G$ is a function $f:V\to \{-1,1,2,\ldots,\lceil\frac{\Delta}{2}\rceil+1\}$ satisfying the conditions… read more here.
Keywords: roman domination; domination graphs; strong roman; signed strong ... See more keywords
Weak Signed Roman Domination in Digraphs
Sign Up to like & getrecommendations! Published in 2021 at "Tamkang Journal of Mathematics"
DOI: 10.5556/j.tkjm.52.2021.3523
Abstract: LetD be a finite and simple digraph with vertex set V (D). A weak signed Roman dominating function (WSRDF) on a digraphD is a function f : V (D) → {−1, 1, 2} satisfying the… read more here.
Keywords: weak signed; signed roman; roman domination; roman ... See more keywords