Results 11 to 20 of about 2,477,819 (60)

Double Roman and double Italian domination [PDF]

, 2023
Let $G$ be a graph with vertex set $V(G)$. A double Roman dominating function (DRDF) on a graph $G$ is a function \( f:V(G)\longrightarrow\{0,1,2,3\} \) that satisfies the following conditions: (i) If $f(v)=0$, then $v$ must have a neighbor $w$ with $f(w)
Volkmann, Lutz, Lutz Volkmann
core   +1 more source

Theoretical results for Perfect Location signed Roman domination problem [PDF]

The study of Roman domination has evolved to encompass a variety of challenging extensions, each contributing to the broader understanding of domination problems in graph theory.
Nikolić, Bojan, Grbić, Milana, Matić, Dragan   +2 more
core   +9 more sources

A note on the double Roman domination number of graphs [PDF]

, 2020
summary:For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least two neighbors assigned $2$ under $f$ or one neighbor with $f(w)
Chen, Xue-Gang
core   +1 more source

Singed Total Domatic Number of a Graph [PDF]

, 2010
The maximum number of functions in a signed total dominating family on G is the signed total domatic number of G. In this paper, some properties related signed total domatic number and signed total domination number of a graph are studied and found the ...
Shailaja S. Shirkol, Walikar, H.B., Kishori P.Narayankar   +2 more
core   +1 more source

Signed Roman Edge k-Domination in Graphs [PDF]

, 2017
Let k ≥ 1 be an integer, and G = (V, E) be a finite and simple graph. The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and all edges having a common end-vertex with e.
Volkmann Lutz, Sheikholeslami Seyed Mahmoud, Asgharsharghi Leila   +2 more
core   +2 more sources

Signed Total Roman Domination in Digraphs [PDF]

, 2017
Let D be a finite and simple digraph with vertex set V (D). A signed total Roman dominating function (STRDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) ∑x∈N−(v)f(x) ≥ 1 for each v ∈ V (D), where N−(v) consists ...
Volkmann Lutz, Volkmann, Lutz
core   +1 more source

Restrained double Roman domination of a graph

, 2022
For a graph G = (V, E), a restrained double Roman dominating function is a function f : V → {0, 1, 2, 3} having the property that if f(v) = 0, then the vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(
Doost Ali Mojdeh, Iman Masoumi, Lutz Volkmann   +2 more
core   +1 more source

Signed Total Roman Edge Domination In Graphs [PDF]

, 2017
Let G = (V,E) be a simple graph with vertex set V and edge set E. A signed total Roman edge dominating function of G is a function f : Ʃ → {−1, 1, 2} satisfying the conditions that (i) Ʃe′∈N(e) f(e′) ≥ 1 for each e ∈ E, where N(e) is the open ...
Sheikholeslami, Seyed Mahmoud, Sheikholeslami Seyed Mahmoud, Leila Asgharsharghi, Asgharsharghi, Leila, Asgharsharghi Leila, Seyed Mahmoud Sheikholeslami   +5 more
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Maximal double Roman domination in graphs

, 2022
A maximal double Roman dominating function (MDRDF) on a graph G = (V, E) is a function f:V(G)→{0,1,2,3} such that (i) every vertex v with f(v)=0 is adjacent to least two vertices assigned 2 or to at least one vertex assigned 3, (ii) every vertex v with f(
Chellali, M., Valenzuela Tripodoro, Juan Carlos, Abdollahzadeh Ahangar, H., Sheikholeslami, S.M.   +3 more
core   +1 more source

Weak signed Roman k-domination in digraphs [PDF]

Let $ k ≥ 1 $ be an integer, and let $ D $ be a finite and simple digraph with vertex set $ V (D) $. A weak signed Roman k-dominating function (WSRkDF) on a digraph $ D $ is a function $ f : V (D) → {−1, 1, 2} $ satisfying the condition that $ \Sigma_{x ...
Volkmann, Lutz
core   +1 more source