2 research outputs found
Radio numbers for generalized prism graphs
A radio labeling is an assignment such that
every distinct pair of vertices 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 number of , , is the minimum span over all
radio labelings of . Generalized prism graphs, denoted , , , have vertex set and
edge set .
In this paper we determine the radio number of for and .
In the process we develop techniques that are likely to be of use in
determining radio numbers of other families of graphs.Comment: To appear in Discussiones Mathematicae Graph Theory. 16 pages, 1
figur
Radio Labelings of Distance Graphs
A radio -labeling of a connected graph is an assignment of non
negative integers to the vertices of such that for any two vertices and , , where is the
distance between and in . In this paper, we study radio labelings of
distance graphs, i.e., graphs with the set of integers as vertex set and
in which two distinct vertices are adjacent if and only if .Comment: 14 page