Abstract The problem of counting spanning trees of graphs or networks is a fundamental and crucial area of research in combinatorics, while has numerous important applications in statistical physics, network theory and theoretical computer science. Very recently, Kosar, Zaman, Ali and Ullah obtained a nice formula on the number of spanning trees of a K5-chain network K5 l constructed by connecting l copys of complete graphs K5. They made extensive use of matrix theory and spectral graph theory, especially the normalized Laplacian of graphs. In this paper, by using a rather simple and more physical treatment (the mesh-star transformation in electrical network) without any linear algebra, we generalize their result to Kn-chain graphs and $K_n$-ring graphs. The results show that there is a simple relation between the number of spanning trees of the 
Kn-chain graph Ln l and the Kn-ring graph Cn l. We also calculate the corresponding tree entropy (or so called "the asymptotic growth constant'') and find that the tree entropy of the corresponding Kn-chain graphs and Kn-ring graphs are totally the same.