Rainbow Connection in Some Brick Product Graphs - Kulkarni Sunita Jagannatharao; R. Murali (International Journal of Mathematics And its Applications, 2017)
Let G be a non-trivial connected graph on which is defined a colouring c: E(G)→ {1,2,3,…,k}, kN of edges of G, where adjacent edges may be coloured the same. A path P in G is a rainbow path if no two edges of P are coloured the same. G is rainbow-connected if it contains a rainbow u-v path for every two vertices u and v of G. The minimum k for which there exists such a k-edge colouring is called rainbow connection number of G, denoted by r_c(G). In this paper we determine r_c(G) for some brick product graphs C(2n,m,r) associated with even cycles for m=2.