On radio connection number of graphs
Discussiones Mathematicae Graph Theory
Received 29.09.2017, Revised 31.07.2018, Accepted 06.12.2018, doi: 10.7151/dmgt.2196
Given a graph G and a vertex coloring c, G is called l-radio connected if between any two distinct vertices u and v there is a path such that coloring c restricted to that path is an l-radio coloring. The smallest number of colors needed to make G l-radio connected is called the l-radio connection number of G. In this paper we introduce these notions and initiate the study of connectivity through radio colored paths, providing results on the 2-radio connection number, also called L(2,1)-connection number: lower and upper bounds, existence problems, exact values for known classes of graphs and graph operations.
radio connection number, radio coloring, L(2,1)-connection number, L(2,1)-connectivity, L(2,1)-labeling