Geodesic
On the Ordering of Trees by the Two Indices
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 4 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, among all the trees with $n$ vertices and $k$ pendent vertices, we determine the trees with the first $[{n-k+1}/{2}]$ largest Merrifield-Simmons index and the trees with the first $[{n-k+1}/{2}]$ smallest Hosoya index.
Classification : 11B39, 05C05. 
@article{BMMS_2012_35_4_a12,
     author = {Chengfu Ye and Zhiquan Hu},
     title = {On the {Ordering} of {Trees} by the {Two} {Indices}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_4_a12/}
}
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Chengfu Ye; Zhiquan Hu. On the Ordering of Trees by the Two Indices. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 4. http://geodesic.mathdoc.fr/item/BMMS_2012_35_4_a12/