根も葉もない

groundless, unsubstantiated 毫无根据的，站不住脚的

Roots give support to a tree much as facts give support to claims or allegations. Leaves show the health of a tree, proving its life and vitality. With either support(root) nor evidence(leaves), the allegation (tree) cannot stand.（I think the analogy here is quite clever)

山田さんの奥さん、浮気(uwaki)してるらしいよ。Mrs. Yamada seem to be having an affair

そんなこと、うそよ。全く(mattaku)根も葉もない(ne mo ha mo nai)いうわさに決まってるわ。
That's not true. A groundless rumour, for sure.