Trees Preserving Wiener Index in Join Graph p_m∨p_(2k+1)

The Wiener index W is the sum of distance between all pairs of vertices of a connected graph.Given a connected graph G if there is a subtree T of G such that W(G)=W(T),then T is a tree preserving the Wiener index of G.This paper shows that some subtrees preserving the Wiener index in the join graph pm∨p2k+1 of order m+2k+1 exist under the following condition:m=t2+4t+8/3k3-k2+4/3k+1(t≥k2-1/2k) and the result contains a known conclusion.