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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, H. Abdollahzadeh Ahangar, R. Khoeilar, S.M. Sheikholeslami   +3 more
doaj   +4 more sources

More results on the signed double Roman domination number of graphs

AKCE International Journal of Graphs and Combinatorics
A signed double Roman dominating function (SDRD-function) on a graph G is defined as a function [Formula: see text] having the property that [Formula: see text] for each [Formula: see text] and if [Formula: see text], then the vertex u must have a ...
Seyed Mahmoud Sheikholeslami, Lutz Volkmann   +1 more
doaj   +5 more sources

Signed double Roman domination numbers in digraphs

Annals of the University of Craiova - Mathematics and Computer Science Series, 2021
"Let $D=(V,A)$ be a finite simple digraph. A signed double Roman dominating function (SDRD-function) on the digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2, 3\}$ satisfying the following conditions: (i) $\sum_{x\in N^-[v]}f(x)\ge 1$ for each $v\in V(D)$, where $N^-[v]$ consist of $v$ and all in-neighbors of $v$, and (ii) if $f(v)=-1$, then the ...
Jafar Amjadi, Fatemeh Pourhosseini
semanticscholar   +4 more sources

Bounds for signed double Roman k-domination in trees [PDF]

RAIRO - Operations Research, 2018
Let k ≥ 1 be an integer and G be a simple and finite graph with vertex set V(G). A signed double Roman k-dominating function (SDRkDF) on a graph G is a function f:V(G) → {−1,1,2,3} such that (i) every vertex v with f(v) = −1 is adjacent to at least two vertices assigned a 2 or to at least one vertex w with f(w) = 3, (ii) every vertex v with f(v) = 1 is
Hong Yang, Pu Wu, S. Nazari-Moghaddam, Seyed Mahmoud Sheikholeslami, Xiaosong Zhang, Zehui Shao, Yuan Yan Tang   +6 more
semanticscholar   +3 more sources

Signed double Roman domination on cubic graphs [PDF]

Applied Mathematics and Computation, 2023
The signed double Roman domination problem is a combinatorial optimization problem on a graph asking to assign a label from $\{\pm{}1,2,3\}$ to each vertex feasibly, such that the total sum of assigned labels is minimized. Here feasibility is given whenever (i) vertices labeled $\pm{}1$ have at least one neighbor with label in $\{2,3\}$; (ii) each ...
Enrico Iurlano, Tatjana Zec, Marko Djukanović, Günther R. Raidl   +3 more
semanticscholar   +5 more sources

Signed double Roman domination in graphs

Discrete Applied Mathematics, 2018
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H. Abdollahzadeh Ahangar, Mustapha Chellali, Seyed Mahmoud Sheikholeslami   +2 more
semanticscholar   +5 more sources

More results on the signed double Roman k-domination in graphs [PDF]

Aequationes mathematicae
Abstract Let $$k\ge 1$$ k ≥ 1 be an integer, and let G be a finite and simple graph with vertex set V(G).
Michael A. Henning, Lutz Volkmann
semanticscholar   +4 more sources

Lower Bounds on Signed Total Double Roman k-domination in Graphs [PDF]

Journal of Mathematical Sciences and Informatics
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L. Shahbazi, H. Abdollahzadeh Ahangar, R. Khoeilar, Seyed Mahmoud Sheikholeslami   +3 more
semanticscholar   +3 more sources

Signed total double Roman dominating functions in graphs

AKCE International Journal of Graphs and Combinatorics
A signed total double Roman dominating function (STDRDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex v with [Formula: see text] has at least two neighbors assigned 2 under f or one neighbor w
L. Shahbazi, H. Abdollahzadeh Ahangar, S. M. Sheikholeslami   +2 more
doaj   +2 more sources

Signed double Italian domination

AIMS Mathematics, 2023
A signed double Italian dominating function (SDIDF) on a graph $ G = (V, E) $ is a function $ f $ from $ V $ to $ \{-1, 1, 2, 3\} $, satisfying (ⅰ) $ \sum_{u\in N[v]}f(u)\ge1 $ for all $ v\in V $; (ⅱ) if $ f(v) = -1 $ for some $ v\in V $, then there ...
Ahlam Almulhim
doaj   +1 more source