Results 21 to 30 of about 862,623 (267)
Vertex–Edge Roman {2}-Domination
MathematicsA vertex–edge Roman {2}-dominating function on a graph G=(V,E) is a function f:V⟶{0,1,2} satisfying that, for every edge uv∈E with f(v)=f(u)=0, ∑w∈N(v)∪N(u)f(w)≥2. The weight of the function f is the sum ∑a∈Vf(a).
Ahlam Almulhim, Saiful Rahman Mondal
doaj +2 more sources
Some Results on the Strong Roman Domination Number of Graphs [PDF]
Mathematics Interdisciplinary Research, 2020 Let G=(V,E) be a finite and simple graph of order n and maximum degree Δ(G). A strong Roman dominating function on a graph G is a function f:V (G)→{0, 1,… ,[Δ(G)/2 ]+ 1} satisfying the condition that every vertex v for which f(v)=0 is
Akram Mahmoodi +2 more
doaj +1 more source
Several Roman domination graph invariants on Kneser graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 This paper considers the following three Roman domination graph invariants on Kneser graphs: Roman domination, total Roman domination, and signed Roman domination.
Tatjana Zec, Milana Grbić
doaj +1 more source
Total double Roman domination in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:V\rightarrow\{0,1,2,3\}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one ...
Guoliang Hao +2 more
doaj +1 more source
On the Quasi-Total Roman Domination Number of Graphs
Mathematics, 2021 Domination theory is a well-established topic in graph theory, as well as one of the most active research areas. Interest in this area is partly explained by its diversity of applications to real-world problems, such as facility location problems ...
Abel Cabrera Martínez +2 more
doaj +1 more source
On [k] -Roman domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 For an integer [Formula: see text] let f be a function that assigns labels from the set [Formula: see text] to the vertices of a simple graph [Formula: see text].
N. Khalili +3 more
doaj +1 more source
Weak signed Roman domination in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 A weak signed Roman dominating function (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as a function $f:V(G)\rightarrow\{-1,1,2\}$ having the property that $\sum_{x\in N[v]}f(x)\ge 1$ for each $v\in V(G)$, where $N[v]$ is the closed ...
Lutz Volkmann
doaj +1 more source
Bounds on signed total double Roman domination [PDF]
Communications in Combinatorics and Optimization, 2020 A signed total double Roman dominating function (STDRDF) on {an} isolated-free graph $G=(V,E)$ is a function $f:V(G)\rightarrow\{-1,1,2,3\}$ such that (i) every vertex $v$ with $f(v)=-1$ has at least two neighbors assigned 2 under $f$ or one neighbor ...
L. Shahbazi +3 more
doaj +1 more source
Edge Roman Domination on Graphs [PDF]
Graphs and Combinatorics, 2016 An edge Roman dominating function of a graph $G$ is a function $f\colon E(G) \rightarrow \{0,1,2\}$ satisfying the condition that every edge $e$ with $f(e)=0$ is adjacent to some edge $e'$ with $f(e')=2$. The edge Roman domination number of $G$, denoted by $γ'_R(G)$, is the minimum weight $w(f) = \sum_{e\in E(G)} f(e)$ of an edge Roman dominating ...
Gerard J. Chang +2 more
openaire +2 more sources
Quadruple Roman Domination in Trees [PDF]
Symmetry, 2021 This paper is devoted to the study of the quadruple Roman domination in trees, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. For any positive integer k, a [k]-Roman dominating function ([k]-RDF) of a simple graph G is a function from the vertex set V of G to the set {0,1,2,…,k+1} if ...
Zheng Kou +4 more
openaire +2 more sources