"Radio labelings of distance graphs"@en . . "10.1016/j.dam.2013.06.024" . "Motivated by the Channel Assignment Problem, we study radio $k$-labelings of graphs. A radio $k$-labeling of a connected graph $G$ is an assignment $c$ of non negative integers to the vertices of $G$ such that $$|c(x) - c(y)| }= k+1 - d(x,y),$$ for any two distinct vertices $x$ and $y$, where $d(x,y)$ is the distance between $x$ and $y$ in $G$. In this paper, we study radio $k$-labelings of distance graphs, i.e., graphs with the set $Z$ of integers as vertex set and in which two distinct vertices $i, j$ in $Z$ are adjacent if and only if $|i - j|$ is in $D$. We give some lower and upper bounds for radio $k$-labelings of distance graphs with distance sets $D={1,2,..., t}$, $D={1,t}$ and $D={t-1,t}$ for any positive integer $t}1$." . "NL - Nizozemsko" . "101336" . . . . "[CC0E14D7CF8D]" . "Holub, P\u0159emysl" . "Ekstein, Jan" . . . "\u010Cada, Roman" . "RIV/49777513:23520/13:43919556!RIV14-MSM-23520___" . . . . "0166-218X" . . "161" . . . "23520" . "Discrete Applied Mathematics" . "Radio labelings of distance graphs" . . "Radio labelings of distance graphs"@en . . "distance graph; radio k-labeling number; Graph labeling"@en . "P(ED1.1.00/02.0090), P(GBP202/12/G061)" . "Radio labelings of distance graphs" . . "3"^^ . . "RIV/49777513:23520/13:43919556" . . . "9"^^ . "18" . "Motivated by the Channel Assignment Problem, we study radio $k$-labelings of graphs. A radio $k$-labeling of a connected graph $G$ is an assignment $c$ of non negative integers to the vertices of $G$ such that $$|c(x) - c(y)| }= k+1 - d(x,y),$$ for any two distinct vertices $x$ and $y$, where $d(x,y)$ is the distance between $x$ and $y$ in $G$. In this paper, we study radio $k$-labelings of distance graphs, i.e., graphs with the set $Z$ of integers as vertex set and in which two distinct vertices $i, j$ in $Z$ are adjacent if and only if $|i - j|$ is in $D$. We give some lower and upper bounds for radio $k$-labelings of distance graphs with distance sets $D={1,2,..., t}$, $D={1,t}$ and $D={t-1,t}$ for any positive integer $t}1$."@en . "4"^^ . . "Togni, Olivier" .