On Algorithms for Enumerating Subtrees of Hexagonal and Phenylene Chains
The Computer Journal
As one of the counting-based topological indices, the number of subtrees and its variations has received much attention in recent years. In this paper, using generating functions, we investigate and derive formulas for this index of hexagonal and phenylene chains. We also present graph-theoretical algorithms for enumerating subtrees of these two chains. Extremal values and graphs with respect to the subtree number among all hexagonal and phenylene chains with n hexagons are also determined. As an application, we briefly examine the subtree densities of these two chains.
Yang, Yu, Hongbo Liu, Hua Wang, Ansheng Deng, Colton Magnant.
"On Algorithms for Enumerating Subtrees of Hexagonal and Phenylene Chains."
The Computer Journal, 60 (5): 690-710.
doi: 10.1093/comjnl/bxw091 source: https://academic.oup.com/comjnl/article/60/5/690/2632622