Results 51 to 60 of about 839 (260)
Algorithm aspect on total Roman $\{2\}$-domination number of Cartesian products of paths and cycles [PDF]
, 2023 A total Roman {2}-dominating function (TR2DF) on a graph G with vertex set V is a function f : V → {0, 1, 2} having the property that for every vertex v with f(v) = 0, ∑u∈N (v) f(u) ≥ 2, where N(v) represents the open neighborhood of v, and the subgraph ...
Qin Chen
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Quasi-total Roman bondage number in graphs
AKCE International Journal of Graphs and Combinatorics, 2022 A quasi-total Roman dominating function (QTRD-function) on [Formula: see text] is a function [Formula: see text] such that (i) every vertex x for which f(x) = 0 is adjacent to at least one vertex v for which f(v) = 2, and (ii) if x is an isolated vertex ...
Huiqin Jiang, Zehui Shao
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Protection of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2022 In this paper, we study the weak Roman domination number and the secure domination number of lexicographic product graphs. In particular, we show that these two parameters coincide for almost all lexicographic product graphs. Furthermore, we obtain tight
Klein Douglas J. +1 more
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Closed formulas for the total Roman domination number of lexicographic product graphs [PDF]
, 2021 Let G be a graph with no isolated vertex and f: V(G) → {0, 1, 2} a function. Let Vi = {x ∈ V(G) : f(x) = i} for every i ∈ {0, 1, 2}. We say that f is a total Roman dominating function on G if every vertex in V0 is adjacent to at least one vertex in V2 ...
Cabrera Martínez, Abel +1 more
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Roman Edge Semi-Total Block Domination of a Graph
Asia Pacific Journal of Mathematics, 2018 Summary: A graph \(G=(V,E)\), semi-total block graph \(T_b(G)=H\), whose set of vertices is the union of the set of vertices and blocks of \(G\) in whose two vertices are adjacent if and only if the corresponding vertices and blocks of \(G\) are adjacent or the corresponding members are incident.
Girish V.R., P. Usha
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Total restrained Roman domination
, 2022 Published by Azabaijan Shahid Madani University, Azarshahr ...
Amjadi, Jafar +2 more
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Total Roman domination edge-critical graphs [PDF]
Involve, a Journal of Mathematics, 2019 A total Roman dominating function on a graph $G$ is a function $% f:V(G)\rightarrow \{0,1,2\}$ such that every vertex $v$ with $f(v)=0$ is adjacent to some vertex $u$ with $f(u)=2$, and the subgraph of $G$ induced by the set of all vertices $w$ such that $f(w)>0$ has no isolated vertices. The weight of $f$ is $Σ_{v\in V(G)}f(v)$.
Lampman, Chloe +2 more
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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
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Signed double Roman domination on cubic graphs [PDF]
, 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.
Iurlano, Enrico +3 more
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Diversity, 2023 Halmyris (Murighiol, Tulcea County, Romania) is one of the most important Roman settlements located in the inferior sector of the Danube Delta, in the easternmost part of Scythia province during the Late Antiquity.
Margareta Simina Stanc +4 more
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