Abstract
There are many kinds of edge colorings. This paper deals with a special edge coloring named rainbow coloring. Different from other edge colorings, the rainbow coloring requires every pair of vertices has a rainbow path between them. A rainbow path is a path \( \, P \, \) in graph \( \, G \, \) such that every edge on P has different color. A rainbow connected graph \( \, G \, \) is a graph such that there is a rainbow path between every pair of vertices. The rainbow connection number, denoted \( rc(G), \) is the smallest number of colors to meet the conditions that the graph \( G \) is rainbow connected. The bubble sort graph, denoted as \( B_{n} , \) is a type of Cayley graph. This paper established the rainbow connection number of bubble sort graph.
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