Geodesic
On Radio Connection Number of Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 3, pp. 705-730

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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.
Keywords: radio connection number, radio coloring, L (2, 1)-connection number, L (2, 1)-connectivity, L (2, 1)-labeling 
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Marinescu-Ghemeci, Ruxandra. On Radio Connection Number of Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 3, pp. 705-730. http://geodesic.mathdoc.fr/item/DMGT_2019_39_3_a7/