The objective of this paper is to propose an algorithm to generate all possible structures of spanning trees of an undirected complete graph of n vertices. The process starts with a star-tree (T) of the given complete graph and then replacing the edges of T one by one to generate different possible structures like chain, branch, etc. These spanning tree structures repeat themselves as we move from lower to higher values of n. The authors have attempted to find out some generalized expressions for different structures of spanning trees for a complete graph of order n. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.