منابع مشابه
On Hop Roman Domination in Trees
Let $G=(V,E)$ be a graph. A subset $Ssubset V$ is a hop dominating setif every vertex outside $S$ is at distance two from a vertex of$S$. A hop dominating set $S$ which induces a connected subgraph is called a connected hop dominating set of $G$. Theconnected hop domination number of $G$, $ gamma_{ch}(G)$, is the minimum cardinality of a connected hopdominating set of $G$...
متن کاملA characterization relating domination, semitotal domination and total Roman domination in trees
A total Roman dominating function on a graph $G$ is a function $f: V(G) rightarrow {0,1,2}$ such that for every vertex $vin V(G)$ with $f(v)=0$ there exists a vertex $uin V(G)$ adjacent to $v$ with $f(u)=2$, and the subgraph induced by the set ${xin V(G): f(x)geq 1}$ has no isolated vertices. The total Roman domination number of $G$, denoted $gamma_{tR}(G)$, is the minimum weight $omega(f)=sum_...
متن کاملCo-Roman domination in trees
Abstract: Let G=(V,E) be a graph and let f:V(G)→{0,1,2} be a function. A vertex v is protected with respect to f, if f(v)>0 or f(v)=0 and v is adjacent to a vertex of positive weight. The function f is a co-Roman dominating function, abbreviated CRDF if: (i) every vertex in V is protected, and (ii) each u∈V with positive weight has a neighbor v∈V with f(v)=0 such that the func...
متن کاملRoman domination excellent graphs: trees
A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V rightarrow {0, 1, 2}$ suchthat every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = Sigma_{vin V} f(v)$The Roman domination number, $gamma_R(G)$, of $G$ is theminimum weight of an RDF on $G$.An RDF of minimum weight is called a $gamma_R$-function.A graph G is said to be $g...
متن کاملOn trees with equal Roman domination and outer-independent Roman domination numbers
A Roman dominating function (RDF) on a graph $G$ is a function $f : V (G) to {0, 1, 2}$satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least onevertex $v$ for which $f(v) = 2$. A Roman dominating function $f$ is called an outer-independentRoman dominating function (OIRDF) on $G$ if the set ${vin Vmid f(v)=0}$ is independent.The (outer-independent) Roman dom...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2019
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2099