| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 427256 | Information Processing Letters | 2015 | 6 Pages |
•Establish a lemma for bounding the rainbow 2-connection numbers of some special graphs.•Provide an upper bound for the rainbow 2-connection numbers of abelian Cayley graphs.•Characterize the rainbow 2-connection numbers of cubic dihedrants.
A path in an edge colored graph is said to be a rainbow path if no two edges on this path share the same color. For an l-connected graph Γ and an integer k with 1≤k≤l1≤k≤l, the rainbow k-connection number of Γ is the minimum number of colors required to color the edges of Γ such that any two distinct vertices of Γ are connected by k internally disjoint rainbow paths. In this paper, a method is provided for bounding the rainbow 2-connection numbers of graphs with certain structural properties. Using this method, we consider the rainbow 2-connection numbers of Cayley graphs, especially, those defined on abelian groups and dihedral groups.
