Related papers: Radio labelling of two-branch trees

A radio labeling of a graph $G$ is a mapping $f: V(G) \rightarrow \{0, 1, 2, \ldots\}$ such that $|f(u)-f(v)|\geq d + 1 - d(u,v)$ for every pair of distinct vertices $u, v$ of $G$, where $d$ is the diameter of $G$ and $d(u,v)$ the distance…

Let $G$ be a finite, connected, undirected graph with diameter $diam(G)$ and $d(u,v)$ denote the distance between $u$ and $v$ in $G$. A radio labeling of a graph $G$ is a mapping $f: V(G) \rightarrow \{0,1,2,...\}$ such that $|f(u)-f(v)|…

For a simple finite connected graph $G$, let $diam(G)$ and $d_{G}(u,v)$ denote the diameter of $G$ and distance between $u$ and $v$ in $G$, respectively. A radio labeling of a graph $G$ is a mapping $f$ : $V(G) \rightarrow \{0, 1, 2,...\}$…

Let $G$ be a simple connected graph. For any two vertices $u$ and $v$, let $d(u,v)$ denote the distance between $u$ and $v$ in $G$, and let $diam(G)$ denote the diameter of $G$. A radio-labeling of $G$ is a function $f$ which assigns to…

A radio labeling of a graph $G$ is a mapping $f$ : $V(G) \rightarrow \{0, 1, 2,...\}$ such that $|f(u)-f(v)| \geq diam(G) + 1 - d(u,v)$ holds for every pair of vertices $u$ and $v$, where $diam(G)$ is the diameter of $G$ and $d(u,v)$ is the…

A radio labelling of a graph $G$ is a mapping $f : V(G) \rightarrow \{0, 1, 2,\ldots\}$ such that $|f(u)-f(v)|\geq diam(G) + 1 - d(u,v)$ for every pair of distinct vertices $u,v$ of $G$, where $diam(G)$ is the diameter of $G$ and $d(u,v)$…

Let $\mathbb{N}$ be the set of positive integers. A radio labeling of a graph $G$ is a mapping $\varphi : V(G) \rightarrow \mathbb{N} \cup \{0\}$ such that the inequality $|\varphi(u)-\varphi(v)| \geq diam(G) + 1 - d(u,v)$ holds for every…

A radio labeling of a graph $G$ is a function $f : V(G) \rightarrow \{0,1,2,\ldots\}$ such that $|f(u)-f(v)| \geq diam(G) + 1 - d(u,v)$ for every pair of distinct vertices $u,v$ of $G$. The radio number of $G$, denoted by $rn(G)$, is the…

A radio labeling of a graph $G$ is a mapping $\vp : V(G) \rightarrow \{0, 1, 2,...\}$ such that $|\vp(u)-\vp(v)|\geq \diam(G) + 1 - d(u,v)$ for every pair of distinct vertices $u,v$ of $G$, where $\diam(G)$ and $d(u,v)$ are the diameter of…

The radio number problem uses a graph-theoretical model to simulate optimal frequency assignments on wireless networks. A radio labeling of a connected graph $G$ is a function $f:V(G) \to \mathbb Z_{0}^+$ such that for every pair of…

A radio labeling of a connected graph $G$ is a function $c:V(G) \to \mathbb Z_+$ such that for every two distinct vertices $u$ and $v$ of $G$ $$\text{distance}(u,v)+|c(u)-c(v)|\geq 1+ \text{diameter}(G).$$ The radio number of a graph $G$ is…

A radio labeling is an assignment $c:V(G) \rightarrow \textbf{N}$ such that every distinct pair of vertices $u,v$ satisfies the inequality $d(u,v)+|c(u)-c(v)|\geq \diam(G)+1$. The span of a radio labeling is the maximum value. The radio…

Let $d(u,v)$ denote the distance between two distinct vertices of a connected graph $G$, and $\diam(G)$ be the diameter of $G$. A radio labeling $c$ of $G$ is an assignment of positive integers to the vertices of $G$ satisfying…

For a connected graph $G$, let $diam(G)$ and $d(u,v)$ denote the diameter of $G$ and distance between $u$ and $v$ in $G$. A radio labeling of a graph $G$ is a mapping $\varphi : V(G) \rightarrow \{0,1,2,...\}$ such that…

The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. In this paper we characterize all trees with radius at most three…

For $G$ a simple, connected graph, a vertex labeling $f:V(G)\rightarrow \mathbb{Z}_+$ is called a $\textit{radio labeling of}$ $G$ if it satisfies $|f(u)-f(v)|\geq \operatorname{diam}(G) + 1 - d(u,v)$ for all distinct vertices $u,v\in…

Radio labeling is a variation of Hale's channel assignment problem, in which one seeks to assign positive integers to the vertices of a graph $G$ subject to certain constraints involving the distances between the vertices. Specifically, a…

An L(2, 1)-labeling of a graph is an assignment of nonnegative integers to the vertices of G such that adjacent vertices receive numbers differed by at least 2, and vertices at distance 2 are assigned distinct numbers. The L(2, 1)-labeling…

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…

The study of radio graceful labelings is motivated by modeling efficient frequency assignment to radio towers, cellular towers, and satellite networks. For a simple, connected graph $G = (V(G), E(G))$, a radio labeling is a mapping $f: V(G)…