One-to-many 3-coverable In The Square Graph

Given an undirected graph G =(V,E),a one-to-many k cover of a graph,defined as the graph exists k internally vertex-disjoint paths that from arbitrary a single source to any k sinks that cover every vertex of graph.In literature [1],Park and others established a sufficient and necessary conditions for the cube of a connected graph,there is a one to many three inside disjoined road cover,which connected a source vertex and three sinks.Because a k-coverable graph needs higher connectivity,he found the the necessary and sufficient condition of the cube of a connected graph is 3 coverable,then he consider lowering the vertex of connectivity,such as the square of a 2 connected graph also has one-to-many 3 coverable.In this paper,we will show that the square of a 2 connected graph is one-tomany 3 coverable.i.e.the square of a 2 connected graph always has a 3-DP C,joins arbitrary a single source to three sinks.