Radio labelings of distance graphs
Motivated by the Channel Assignment Problem, we study radio k k -labelings of graphs. A radio k k -labeling of a connected graph G G is an assignment c c of non-negative integers to the vertices of G G such that In this paper, we study radio k k -labelings of distance graphs, i.e., graphs with the set Z Z of integers as vertex set and in which two distinct vertices i,j?Z i , j ? Z are adjacent if and only if |i?j|?D | i ? j | ? D . We give some lower and upper bounds for radio k k -labelings of distance graphs with distance sets D(1,2,,t) D ( 1 , 2 ,  , t ) , D(1,t) D ( 1 , t ) and D(t?1,t) D ( t ? 1 , t ) for any positive integer t>1 t > 1 .
distance graph graph labeling radio k k -labeling number k k k k k