Related papers: Boundary Independent Broadcasts in Graphs

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 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 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…

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…

In 2001, D. Erwin \cite{Erw01} introduced in his Ph.D. dissertation the notion of broadcast independence in unoriented graphs. Since then, some results but not many, are published on this notion, including research work on the broadcast…

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=(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…

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 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…

A broadcast on a connected graph is a function f that assigns each vertex v an integer f(v) with 0 <= f(v) <= ecc(v) where ecc(v) denotes the eccentricity of v. A vertex u hears a broadcasting vertex v (with f(v)>0) if u is at distance at…

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…

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 $d(u,v) \leq f(v)$.…

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…

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 $G$.…

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 function $f:V(G)\rightarrow \mathbb{Z}^+ \cup \{0\}$ is a resolving broadcast of a graph $G$ if, for any distinct $x,y\in V(G)$, there exists a vertex $z\in V(G)$ with $f(z)>0$ such that $\min\{d(x,z), f(z)+1\} \neq \min\{d(y,z),…

Let $G=( V(G), E(G) )$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. We say a subset $D$ of $V(G)$ dominates $G$ if every vertex in $V \setminus D$ is adjacent to a vertex in $D$. A generalization of this concept is…