Results 31 to 40 of about 838 (256)
Signed total strong Roman domination in graphs [PDF]
Discrete Mathematics Letters, 2022 Maryam Hajjari +1 more
doaj +2 more sources
Bounds on weak roman and 2-rainbow domination numbers
Discrete Applied Mathematics, 2014 We mainly study two related dominating functions, namely, the weak Roman and 2-rainbow dominating functions. We show that for all graphs, the weak Roman domination number is bounded above by the 2-rainbow domination number.
TERESA W Haynes, Stephen T Hedetniemi
exaly +2 more sources
Total Roman Reinforcement in Graphs
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2 and the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex.
Ahangar H. Abdollahzadeh +4 more
doaj +2 more sources
On the Outer Independent Total Double Roman Domination in Graphs [PDF]
Mediterranean Journal of Mathematics, 2023 A double Roman dominating function (DRDF) on a graph G=(V, E) is a function f:V→ {0,1,2,3} satisfying (i) if f(v)=0, then there must be at least two neighbors assigned 2 under f or one neighbor w with f(w)=3; and (ii) if f(v)=1 then v must be adjacent to
H. Abdollahzadeh Ahangar +7 more
core +4 more sources
Bounds on the total double Roman domination number of graphs
Discussiones Mathematicae Graph Theory, 2023 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 ...
Xie, Zhihong +7 more
core +2 more sources
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
Total Roman domination subdivision number in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$.
Jafar Amjad
doaj +1 more source
Maximum Second Zagreb Index Of Trees With Given Roman Domination Number [PDF]
Transactions on Combinatorics, 2023 Chemical study regarding total $\pi$-electron energy with respect to conjugated molecules has focused on the second Zagreb index of graphs. Moreover, in the last half-century, it has gotten a lot of attention.
Ayu Ameliatul Ahmad Jamri +3 more
doaj +1 more source
Total Roman {2}-domination in graphs [PDF]
Quaestiones Mathematicae, 2019 Given a graph $G=(V,E)$, a function $f:V\rightarrow \{0,1,2\}$ is a total Roman $\{2\}$-dominating function if: (1) every vertex $v\in V$ for which $f(v)=0$ satisfies that $\sum_{u\in N(v)}f(u)\geq 2$, where $N(v)$ represents the open neighborhood of $v$, and (2) every vertex $x\in V$ for which $f(x)\geq 1$ is adjacent to at least one vertex $y\in V ...
Suitberto Cabrera García +3 more
openaire +3 more sources
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 +3 more
core +2 more sources