Related papers: Broadcast independence number of oriented circulan…

An independent broadcast on a graph $G$ is a function $f: V \longrightarrow \{0,\ldots,{\rm diam}(G)\}$ such that $(i)$ $f(v)\leq e(v)$ for every vertex $v\in V(G)$, where $\operatorname{diam}(G)$ denotes the diameter of $G$ and $e(v)$ the…

A broadcast on a nontrivial connected graph G is a function f from the vertices of G to the non-negative integers such that f(v) does not exceed e(v) (the eccentricity of v) for each vertex v. If G is disconnected, we define a broadcast on…

A broadcast on a graph $G=(V,E)$ is a function $f: V\longrightarrow \{0,\ldots,\operatorname{diam}(G)\}$ such that $f(v)\leq e\_G(v)$ for every vertex $v\in V$, where$\operatorname{diam}(G)$ denotes the diameter of $G$ and $e\_G(v)$ the…

An independent broadcast on a connected graph $G$ is a function $f:V(G)\to \mathbb{N}_0$ such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$, and $f(x)>0$ implies that $f(y)=0$ for every vertex…

A broadcast on a nontrivial connected graph G with vertex set V is a function f from V to {0,1,...,diam(G)} such that f(v) is at most the eccentricity of v for all v in V. The weight of f is the sum of the function values taken over V. A…

An independent broadcast on a connected graph $G$ is a function $f:V(G)\to \mathbb{N}_0$ such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$, and $f(x)>0$ implies that $f(y)=0$ for every vertex…

Let $G$ be a simple undirected graph.A broadcast on $G$ isa function $f : V(G)\rightarrow\mathbb{N}$ such that $f(v)\le e\_G(v)$ holds for every vertex $v$ of $G$, where $e\_G(v)$ denotes the eccentricity of $v$ in $G$, that is, the maximum…

An independent broadcast on a connected graph $G$ is a function $f:V(G)\to \mathbb{N}_0$ such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$, and $f(x)>0$ implies that $f(y)=0$ for every vertex…

A broadcast on a connected graph G with vertex set V(G) is a function $f:V(G)\rightarrow \{0, 1, ..., \text{diam}(G)\}$ such that $f(v)\leq e(v)$ (the eccentricity of $v$) for all $v\in V$. A vertex $v$ is said to be broadcasting if…

A broadcast on a nontrivial connected graph G=(V,E) is a function f from V(G) to {0,1,...,diam(G)} such that f(v) does not exceed the eccentricity of v. The cost of f is the sum of the function values. A broadcast f is dominating if each…

A broadcast on a connected graph $G=(V,E)$ is a function $f:V\rightarrow \{0,1,\dots,\operatorname{diam}(G)\}$ such that $f(v)\leq e(v)$ (the eccentricity of $v$) for all $v\in V$ if $|V|\geq2$, and $f(v)=1$ if $V=\{v\}$. The cost of $f$ is…

A broadcast on a nontrivial connected graph G with vertex set V is a function f from V to {0,1,...,diam(G)} such that f(v) is at most the eccentricity of v for all vertices v. The weight of f is the sum of the function values taken over V.…

A dominating broadcast on a graph G with vertex set V is a function f that maps V to {0,1,...,diam(G)} such that f(v) does not exceed e(v) (the eccentricity of v) for all vertices v, and each vertex u is at distance at most f(v) from a…

Let $G$ be a simple undirected graph.A broadcast on $G$ isa function $f : V(G) \to \mathbf{N}$ such that $f(v)\le e_G(v)$ holds for every vertex $v$ of $G$, where $e_G(v)$ denotes the eccentricity of $v$ in $G$, that is, the maximum…

A broadcast on a nontrivial connected graph G is a function f from V(G) to the set {0,1,...,diam(G)} such that f(v) is at most the eccentricity of v for all vertices v of G. The weight of f is the sum of the function values over V(G). A…

For a graph $G$, a function $f:V(G) \to \{0,1,2\}$ is called a $2$-limited dominating broadcast on $G$ if for every vertex $u$, there exists a vertex $v$ such that $f(v)>0$ and the distance between $u$ and $v$ in $G$ is at most $f(v)$. The…

A broadcast on a graph $G=(V,E)$ is a function $f:V \rightarrow \{0,1, \ldots, \text{diam}(G)\}$ satisfying $f(v) \leq e(v)$ for all $v \in V$, where $e(v)$ denotes the eccentricity of $v$ and $\text{diam}(G)$ denotes the diameter of $G$.…

Given a graph $G=(V,E)$ of diameter $d$, a broadcast is a function $f:V(G) \to \{ 0, 1, \dots, d \}$ where $f(v)$ is at most the eccentricity of $v$. A vertex $v$ is broadcasting if $f(v)>0$ and a vertex $u$ hears $v$ if $d(u,v) \leq f(v)$.…

For a graph $ G = (V, E) $ with a vertex set $ V $ and an edge set $ E $, a function $ f : V \rightarrow \{0, 1, 2, . . . , diam(G)\} $ is called a \emph{broadcast} on $ G $. For each vertex $ u \in V $, if there exists a vertex $ v $ in $…

A dominating set of a graph $G$ is a set of vertices that contains at least one endpoint of every edge on the graph. The domination number of $G$ is the order of a minimum dominating set of $G$. The $(t,r)$ broadcast domination is a…