Results 41 to 50 of about 700 (247)
Roman domination in direct product graphs and rooted product graphs1 [PDF]
, 2021 Let G be a graph with vertex set V(G). A function f : V(G) -> {0, 1, 2) is a Roman dominating function on G if every vertex v is an element of V(G) for which f(v) = 0 is adjacent to at least one vertex u is an element of V(G) such that f(u) = 2.
González Yero, Ismael +3 more
core +1 more source
Total Roman 2-Reinforcement of Graphs
Journal of Mathematics, 2021 A total Roman 2-dominating function (TR2DF) on a graph Γ=V,E is a function l:V⟶0,1,2, satisfying the conditions that (i) for every vertex y∈V with ly=0, either y is adjacent to a vertex labeled 2 under l, or y is adjacent to at least two vertices labeled
M. Kheibari +3 more
doaj +1 more source
Quasi total double Roman domination in graphs
AKCE International Journal of Graphs and CombinatoricsA quasi total double Roman dominating function (QTDRD-function) on a graph [Formula: see text] is a function [Formula: see text] having the property that (i) if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w
S. Kosari +4 more
doaj +1 more source
Total Roman domination in the lexicographic product of graphs [PDF]
, 2019 A total Roman dominating function of a graph $G=(V,E)$ is a function $f: V(G)\to \{0,1,2\}$ such that for every vertex $v$ with $f(v)=0$ there exists a vertex $u$ adjacent to $v$ with $f(u)=2$, and such that the subgraph induced by the set of vertices ...
Campanelli, Nicolás +3 more
core +1 more source
Total Weak Roman Domination in Graphs [PDF]
, 2019 Given a graph G = ( V , E ) , a function f : V → { 0 , 1 , 2 , ⋯ } is said to be a total dominating function if ∑ u ∈ N ( v ) f ( u ) > 0 for every v ∈ V , where N ( v ) denotes the open ...
Juan A. Rodríguez-Velázquez +2 more
core +1 more source
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.
openaire +2 more sources
On the {2}-domination number of graphs [PDF]
, 2022 [EN] Let G be a nontrivial graph and k ¿ 1 an integer. Given a vector of nonnegative integers w = (w0,...,wk), a function f : V(G) ¿ {0,..., k} is a w-dominating function on G if f(N(v)) ¿ wi for every v ¿ V(G) such that f(v) = i. The w-domination number
Cabrera Martínez, Abel +2 more
core +1 more source
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 +1 more source
On the Outer Independent Total Double Roman Domination in Graphs [PDF]
, 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 +1 more source
Advanced Materials, EarlyView.This work develops bias‐triggered conductivity relaxation as a novel technique to study oxygen reactions in mixed ionic‐electronic conducting thin films by integrating electrochemical titration and electrical conductivity relaxation to achieve synchronous multi‐parameter characterization, providing simultaneous electronic, ionic, and extraordinarily ...
Alexander Stangl +4 more
wiley +1 more source