Results 11 to 20 of about 8,636,707 (226)

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

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}.
Ana Almerich-Chulia, Almerich-Chulia, Ana, Cabrera Martinez, Abel, Pedro Martin-Concepcion, Hernandez Mira, Frank Angel, Abel Cabrera Martínez, Frank Angel Hernández Mira, Martín Concepcion, Pedro Efrén   +7 more
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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

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

On Roman, Global and Restrained Domination in Graphs [PDF]

, 2010
In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible.
Zverovich, Vadim, V. Zverovich, Poghosyan, Anush, A. Poghosyan   +3 more
core   +1 more source

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

Total Perfect Roman Domination

, 2023
A total perfect Roman dominating function (TPRDF) on a graph G=(V,E) is a function f from V to {0,1,2} satisfying (i) every vertex v with f(v)=0 is a neighbor of exactly one vertex u with f(u)=2; in addition, (ii) the subgraph of G that is induced by the
Ahlam Almulhim
core   +1 more source

On the Roman Edge Domination Number of a Graph [PDF]

, 2010
Let G be a simple graph with vertex set V (G) and edge set E(G)
K. Ebadi, Ebadi, K., Khodadadi, E., E. Khodadadi, L. Pushpalatha, Pushpalatha, L.   +5 more
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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

Some Properties of Double Roman Domination

, 2020
A double Roman dominating function on a graph G is a function f:VG⟶0,1,2,3 satisfying the conditions that every vertex u for which fu=0 is adjacent to at least one vertex v for which fv=3 or two vertices v1 and v2 for which fv1=fv2=2 and every vertex u ...
Xiaoqing Zhou, Hong Yang
core   +1 more source