Discussiones Mathematicae Graph Theory (Aug 2019)

On Radio Connection Number of Graphs

  • Marinescu-Ghemeci Ruxandra

DOI
https://doi.org/10.7151/dmgt.2196
Journal volume & issue
Vol. 39, no. 3
pp. 705 – 730

Abstract

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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.

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