Some Graphs with Minimum Hosoya Index and Maximum Merrifield-Simmons Index

@inproceedings{Pan2007SomeGW,
  title={Some Graphs with Minimum Hosoya Index and Maximum Merrifield-Simmons Index},
  author={Xiang-Feng Pan and Jun-Ming Xu and Chao Ping Yang and Min-jie Zhou},
  year={2007}
}
The Hosoya index of a graph is defined as the total number of the matchings of the graph and the Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph. In this paper, we obtain the graphs with minimum Hosoya index among the trees with n vertices and diameter d. The extremal graphs is the same as ones given by X. Liet al with maximum Merrifield-Simmons index among such a class of graphs. Also, we give the graphs with both minimum Hosoya index and… CONTINUE READING