Radio labelings of distance graphs
Copyright policy )Radio labelings of distance 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 $$|c(x) - c(y)| \geq k+1 - d(x,y),$$ for any two vertices $x$ and $y$, $x\ne y$, where $d(x,y)$ is the distance between $x$ and $y$ in $G$. In this paper, we study radio 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 $|i - j| \in D$.
14 pages
Distance in graphs, 05C12, 05C78, graph labeling, [ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM], radio \(k\)-labeling number, Channel models (including quantum) in information and communication theory, distance graph, Graph labelling (graceful graphs, bandwidth, etc.), [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], radio k-labeling number, FOS: Mathematics, Mathematics - Combinatorics, distance graph., Combinatorics (math.CO), MSC 05C12, 05C78
Distance in graphs, 05C12, 05C78, graph labeling, [ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM], radio \(k\)-labeling number, Channel models (including quantum) in information and communication theory, distance graph, Graph labelling (graceful graphs, bandwidth, etc.), [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], radio k-labeling number, FOS: Mathematics, Mathematics - Combinatorics, distance graph., Combinatorics (math.CO), MSC 05C12, 05C78
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