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Total Roman {2}-Dominating Functions in Graphs
Discussiones Mathematicae Graph Theory, 2022 A Roman {2}-dominating function (R2F) is a function f : V → {0, 1, 2} with the property that for every vertex v ∈ V with f(v) = 0 there is a neighbor u of v with f(u) = 2, or there are two neighbors x, y of v with f(x) = f(y) = 1.
Ahangar H. Abdollahzadeh +3 more
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Varieties of Roman domination II
AKCE International Journal of Graphs and Combinatorics, 2020 In this work, we continue to survey what has been done on the Roman domination. More precisely, we will present in two sections several variations of Roman dominating functions as well as the signed version of some of these functions.
M. Chellali +3 more
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Strong Equality of Perfect Roman and Weak Roman Domination in Trees [PDF]
, 2019 Let G=(V,E) be a graph and f:V⟶{0,1,2} be a function. Given a vertex u with f(u)=0, if all neighbors of u have zero weights, then u is called undefended with respect to f.
Alhevaz, Abdollah +3 more
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Discrete Mathematics, 2004 The paper studies the Roman domination in graphs. It is a special kind of domination whose introduction was motivated by military rules of the ancient Roman Empire. Let \(G\) be a graph with vertex set \(V(G)\), and let \(f: V(G)\to \{0,1,2\}\). If to each vertex \(v\) with \(f(v)= 0\) there exists a vertex \(w\) with \(f(w)= 2\) adjacent to \(v ...
Cockayne, Ernie J +3 more
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Domination parameters with number 2: Interrelations and algorithmic consequences [PDF]
, 2018 In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination ...
Bonomo, Flavia +4 more
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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
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Graphs with Large Hop Roman Domination Number [PDF]
Computer Science Journal of Moldova, 2019 A subset $S$ of vertices of a graph $G$ is a hop dominating set if every vertex outside $S$ is at distance two from a vertex of $S$. A Roman dominating function on a graph $G=(V,E)$ is a function $f: V(G) \longrightarrow \{0, 1, 2\}$ satisfying the ...
E. Shabani, N. Jafari Rad, A. Poureidi
doaj
Roman Domination in Complementary Prism Graphs [PDF]
, 2012 A Roman domination function on a complementary prism graph GGc is a function f : V [ V c ! {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number R(GGc) of a graph G = (V,E) is the minimum of Px2V [V c f(x)
Chaitra, V., Chaluvaraju, B.
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Discrete Applied Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Beeler, Robert A. +2 more
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Coloring, location and domination of corona graphs [PDF]
, 2012 A vertex coloring of a graph $G$ is an assignment of colors to the vertices of $G$ such that every two adjacent vertices of $G$ have different colors. A coloring related property of a graphs is also an assignment of colors or labels to the vertices of a ...
Aguilar, A. Rondón +2 more
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