The Radio Number of $C_n \square C_n$

Details The Radio Number of $C_n \square C_n$ The Radio Number of $C_n \square C_n$

2010-07-29

arxiv.org/abs/1007.5344v1

Mathematics

Combinatorics

To appear in Ars Combinatoria, 15 pages

Scientific paper

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 radio labeling of a connected graph $G$ is a function $c:V(G) \rightarrow \mathbb Z_+$ such that $$d(u,v)+|c(u)-c(v)|\geq 1+\text{diam}(G)$$ for every two distinct vertices $u$ and $v$ of $G$ (where $d(u,v)$ is the distance between $u$ and $v$). The span of a radio labeling is the maximum integer assigned to a vertex. The radio number of a graph $G$ is the minimum span, taken over all radio labelings of $G$. This paper establishes the radio number of the Cartesian product of a cycle graph with itself (i.e., of $C_n\square C_n$.)

Affiliated with

Also associated with

No associations

Rating

The Radio Number of $C_n \square C_n$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Radio Number of $C_n \square C_n$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Radio Number of $C_n \square C_n$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-699620