Outer-independent total roman domination

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Relating the Outer-Independent Total Roman Domination Number with Some Classical Parameters of Graphs [PDF]

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 ,
Dorota Kuziak, Ismael G Yero, Abel Cabrera Martinez +2 more
exaly +7 more sources

On the Outer Independent Total Double Roman Domination in Graphs [PDF]

Mediterranean Journal of Mathematics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mustapha Chellali +2 more
exaly +6 more sources

Outer-independent total Roman domination in graphs [PDF]

Discrete Applied Mathematics, 2019
Given a graph $G$ with vertex set $V$, a function $f:V\rightarrow \{0,1,2\}$ is an outer-independent total Roman dominating function on $G$ if \begin{itemize} \item every vertex $v\in V$ for which $f(v)=0$ is adjacent to at least one vertex $u\in V$ such that $f(u)=2$, \item every vertex $x\in V$ for which $f(x)\ge 1$ is adjacent to at least one vertex
Dorota Kuziak, Ismael G Yero, Abel Cabrera Martinez +2 more
exaly +5 more sources

Computational Complexity of Outer-Independent Total and Total Roman Domination Numbers in Trees

IEEE Access, 2018
An outer-independent total dominating set (OITDS) of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent.
Zepeng Li +4 more
doaj +4 more sources

On the outer independent total double Roman dominating functions

Let $\{0,1,\dots, t\}$ be abbreviated by $[t].$ A double Roman dominating function (DRDF) on a graph $Γ=(V,E)$ is a map $l:V\rightarrow [3]$ satisfying \textrm{(i)} if $l(r)=0$ then there must be at least two neighbors labeled 2 under $l$ or a neighbor $r'$ with $l(r')=3$; and \textrm{(ii)} if $l(r)=1$ then $r$ must be adjacent to a vertex $r'$ such ...
Ahangar, H. Abdolahzadeh +3 more
openaire +2 more sources

The En-Gedi Spring Site and the Judahite Expansion into the Judaean Desert in the Late Iron Age. [PDF]