Rainbow Colorings on WK-recursive Pyramids

Abstract

A path P is a rainbow path if P with all edges of different colors. An edge coloring graph G is rainbow connected if every two vertices are connected by a rainbow path. An edge coloring under which G is rainbow connected is a rainbow coloring. Rainbow connection number of G is the minimum number of colors needed under a rainbow coloring. In this paper, we propose linear-time algorithms for constructing rainbow colorings on WK-recursive networks and WK-recursive pyramids and thus establish upper bounds to the size of the rainbow connection numbers on WK-recursive networks and WK-recursive pyramids.