The Hosoya Index and Merrifield-Simmons Index of Two Kinds Special Graphs

For a graph, the Hosoya index is referred to as the sums amount about that the matchings of the graph, while, the Merrifield-Simmons index is referred to as the sums about that the independent sets of the graph, The main structure of the paper is two kinds of special graphs \(P_{m,n}^k\) and \(C_{m,n}^k\), then its number of Hosoya index and Merrifield-Simmons index was calculated, and give the corresponding calculation formulas.