Results 11 to 20 of about 86,729 (238)
On the Total Double Roman Domination
IEEE Access, 2019 Let G = (V, E) be a simple graph. A double Roman dominating function (DRDF) on G is a function f from the vertex set V of G into {0, 1, 2, 3} such that if f (u) = 0, then u must have at least two neighbors assigned 2 or one neighbor assigned 3 under f ...
Zehui Shao +3 more
doaj +3 more sources
Further Results on the Total Roman Domination in Graphs
Mathematics, 2020 Let G be a graph without isolated vertices. A function f : V ( G ) → { 0 , 1 , 2 } is a total Roman dominating function on G if every vertex v ∈ V ( G ) for which f ( v ) = 0 is adjacent to at least one vertex u ...
Abel Cabrera Martínez +2 more
doaj +3 more sources
On the signed total Roman domination and domatic numbers of graphs
Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lutz Volkmann
openaire +4 more sources
Bounds on the total double Roman domination number of graphs
Discussiones Mathematicae Graph Theory, 2023 Summary: Let \(G\) be a simple graph with no isolated vertex and let \(\gamma_{tdR}(G)\) be the total double Roman domination number of \(G\). In this paper, we present lower and upper bounds on \(\gamma_{tdR}(G)\) of a graph \(G\) in terms of the order, open packing number and the numbers of support vertices and leaves, and we characterize all ...
Hao, Guoliang +3 more
openaire +1 more source
Quasi-total Roman bondage number in graphs
AKCE International Journal of Graphs and Combinatorics, 2022 A quasi-total Roman dominating function (QTRD-function) on [Formula: see text] is a function [Formula: see text] such that (i) every vertex x for which f(x) = 0 is adjacent to at least one vertex v for which f(v) = 2, and (ii) if x is an isolated vertex ...
Huiqin Jiang, Zehui Shao
doaj +1 more source
On the signed strong total Roman domination number of graphs
Tamkang Journal of Mathematics, 2022 Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximumdegree $\Delta$. A signed strong total Roman dominating function ona graph $G$ is a function $f:V(G)\rightarrow\{-1, 1,2,\ldots, \lceil\frac{\Delta}{2}\rceil+1\}$ satisfying the condition that (i) forevery vertex $v$ of $G$, $f(N(v))=\sum_{u\in N(v)}f(u)\geq 1$, where$N(v)$ is the open ...
Mahmoodi, A., Atapour, M., Norouzian, S.
openaire +1 more source
On the total Roman domination stability in graphs
AKCE International Journal of Graphs and Combinatorics, 2021 A total Roman dominating function on a graph G is a function satisfying the conditions: (i) every vertex u with f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2; (ii) the subgraph induced by the vertices assigned non-zero values has ...
Ghazale Asemian +3 more
doaj +1 more source
Closed formulas for the total Roman domination number of lexicographic product graphs
Ars Mathematica Contemporanea, 2021 Let G be a graph with no isolated vertex and f: V(G) → {0, 1, 2} a function. Let Vi = {x ∈ V(G) : f(x) = i} for every i ∈ {0, 1, 2}. We say that f is a total Roman dominating function on G if every vertex in V0 is adjacent to at least one vertex in V2 and the subgraph induced by V1 ∪ V2 has no isolated vertex.
Cabrera Martínez, Abel +1 more
openaire +5 more sources
Mediterranean Journal of Mathematics, 2022 AbstractFor a given graph G without isolated vertex we consider a function $$f: V(G) \rightarrow \{0,1,2\}$$ f : V ( G ) → { 0 ,
Abel Cabrera Martínez +2 more
openaire +4 more sources