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Article

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

by 1,2, 3,*, 4,5,*, 2 and 2
1
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
2
School of Computer Science, Pingdingshan University, Pingdingshan 467000, China
3
School of Mathematics and Statistics Science, Pingdingshan University, Pingdingshan 467000, China
4
College of Software, Nankai University, Tianjin 300071, China
5
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(5), 472; https://doi.org/10.3390/math7050472
Received: 18 April 2019 / Revised: 17 May 2019 / Accepted: 20 May 2019 / Published: 24 May 2019
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
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. View Full-Text
Keywords: subtree; generating function; fan graph; wheel graph; “partitions” of wheel graph subtree; generating function; fan graph; wheel graph; “partitions” of wheel graph
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MDPI and ACS Style

Yang, Y.; Wang, A.; Wang, H.; Zhao, W.-T.; Sun, D.-Q. On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution. Mathematics 2019, 7, 472. https://doi.org/10.3390/math7050472

AMA Style

Yang Y, Wang A, Wang H, Zhao W-T, Sun D-Q. On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution. Mathematics. 2019; 7(5):472. https://doi.org/10.3390/math7050472

Chicago/Turabian Style

Yang, Yu, An Wang, Hua Wang, Wei-Ting Zhao, and Dao-Qiang Sun. 2019. "On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution" Mathematics 7, no. 5: 472. https://doi.org/10.3390/math7050472

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