A survey on rainbow (vertex-)index of graphs.

The concept of rainbow connection was introduced by Chartrand et al. in 2008. The k -rainbow index, which is a generalization of rainbow connection number was also introduced by Chartrand et al. in 2010. These two new graph-parameters are defined for all edge-colored graphs. Krivelevich and Yuster in 2010 naturally introduced the rainbow vertex-connection number which is defined on vertex-colored graphs. As a natural counterpart of the k -rainbow index and a generalization of rainbow vertex-connection number, Mao introduced the concept of k -vertex-rainbow index in 2016. Nowadays they have become new and active subjects in graph theory. In this survey we attempt to bring together most of the basic and new results that dealt with the k -rainbow index and k -vertex-rainbow index. [ABSTRACT FROM AUTHOR]