Radio Labelings of Distance Graphs

Original · EN

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 vertices x and y, x≠ 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 of integers as vertex set and in which two distinct vertices i, j ∈ are adjacent if and only if |i - j| ∈ D.