Graphs with Large Locating Rainbow Vertex Connection Number - Tita Maryati; Fawwaz Fakhrurrozi Hadiputra ((IJCSAM) International Journal of Computing Science and Applied Mathematics, 2026)
The locating rainbow vertex connection number of G, denoted by rvcl(G), is the least positive integer k such that there exists a k-coloring of G that ensures G is rainbow vertex-connected and each vertex has a distinct rainbow code. To learn how this parameter behave in graphs, it is natural to consider the extremal case. In this paper, we investigate several graphs with the difference of its order and its locating rainbow vertex connection number is not larger than three, i.e. rvcl(G) ∈ {n, n − 1, n − 2, n − 3} for graphs of order n.Furthermore, we demonstrate the existence of a graph with arbitrary large difference of its partition dimension and its locating rainbow vertex connection number. The study provides an overview of some structures that distinguishability under chromatic constraints becomes most costly, as in large number of colors needed.