Rainbow connection numbers of Cayley graphs

Yingbin Ma () and Zaiping Lu ()
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Yingbin Ma: Henan Normal University
Zaiping Lu: Nankai University

Journal of Combinatorial Optimization, 2017, vol. 34, issue 1, No 12, 182-193

Abstract: Abstract An edge colored graph is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number, rc-number for short, of a graph $${\varGamma }$$ Γ , is the smallest number of colors that are needed in order to make $${\varGamma }$$ Γ rainbow connected. In this paper, we give a method to bound the rc-numbers of graphs with certain structural properties. Using this method, we investigate the rc-numbers of Cayley graphs, especially, those defined on abelian groups and on dihedral groups.

Keywords: Edge-coloring; Rainbow connection number; Cayley graph; Dihedral group; Interconnection networks; 05C15; 05C40 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-016-0052-6

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