Solutions to conjectures on the (k,ℓ)‐rainbow index of complete graphs
Qingqiong Cai, Xueliang Li, Jiangli Song · Networks · 2013
The ‐rainbow index of a graph G was introduced by Chartrand et al. (Network 54(2) (2009), 75–81; 55 (2010), 360–367). For the complete graph Kn of order , they showed that for . Furthermore, they conjectured that for every positive integer , there exists a positive integer N such that for every integer . More generally, they conjectured that for every pair of positive integers k and with , there exists a positive integer N such that for every integer . This article provides solutions to these conjectures. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 62(3), 220–224 2013