Authentication of users in an automated business transaction is commonly realized by means of a Public Key Infrastructure(PKI). A PKI is a framework on which the security services are built. Each user or end entity is given a digitally signed data structure called digital certificate. Peer-to- Peer(also called Mesh PKI) architecture is one of the most popular PKI trust models that is widely used in automated business transactions, but certificate path verification is very complex since there are multiple paths between users and the certification path is bidirectional. In this paper, we propose a novel method to convert a peer-to-peer PKI to a Depth First Search(DFS) spanning tree to simplify the certificate path verification by avoiding multiple paths between users, since the DFS spanning tree equivalent of peer-to-peer PKI contains only one path between any two Certification Authorities.