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Rainbow Connection and Graph Products

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Abstract

A path in an edge colored graph G is called a rainbow path if all its edges have pairwise different colors. Then G is rainbow connected if there exists a rainbow path between every pair of vertices of G and the least number of colors needed to obtain a rainbow connected graph is the rainbow connection number. If we demand that there must exist a shortest rainbow path between every pair of vertices, we speak about strongly rainbow connected graph and the strong rainbow connection number. In this paper we study the (strong) rainbow connection number on the direct, strong, and lexicographic product and present several upper bounds for these products that are attained by many graphs. Several exact results are also obtained.

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Authors and Affiliations

  1. Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000, Ljubljana, Slovenia

    Tanja Gologranc, Gašper Mekiš & Iztok Peterin

  2. University of Maribor, FEECS, Smetanova 17, 2000, Maribor, Slovenia

    Iztok Peterin

Authors
  1. Tanja Gologranc
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  2. Gašper Mekiš
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  3. Iztok Peterin
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Correspondence to Iztok Peterin.

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Gologranc, T., Mekiš, G. & Peterin, I. Rainbow Connection and Graph Products. Graphs and Combinatorics 30, 591–607 (2014). https://doi.org/10.1007/s00373-013-1295-y

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  • DOI: https://doi.org/10.1007/s00373-013-1295-y

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