On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution

Yu Yang, An Wang, Hua Wang, Wei-Ting Zhao and Dao-Qiang Sun
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Yu Yang: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
An Wang: School of Mathematics and Statistics Science, Pingdingshan University, Pingdingshan 467000, China
Hua Wang: College of Software, Nankai University, Tianjin 300071, China
Wei-Ting Zhao: School of Computer Science, Pingdingshan University, Pingdingshan 467000, China
Dao-Qiang Sun: School of Computer Science, Pingdingshan University, Pingdingshan 467000, China

Mathematics, 2019, vol. 7, issue 5, 1-19

Abstract: The number of subtrees, or simply the subtree number, is one of the most studied counting-based graph invariants that has applications in many interdisciplinary fields such as phylogenetic reconstruction. Motivated from the study of graph surgeries on evolutionary dynamics, we consider the subtree problems of fan graphs, wheel graphs, and the class of graphs obtained from “partitioning” wheel graphs under dynamic evolution. The enumeration of these subtree numbers is done through the so-called subtree generation functions of graphs. With the enumerative result, we briefly explore the extremal problems in the corresponding class of graphs. Some interesting observations on the behavior of the subtree number are also presented.

Keywords: subtree; generating function; fan graph; wheel graph; “partitions” of wheel graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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