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

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 p...

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Published in:Mathematics (Basel) 2019-05, Vol.7 (5), p.472
Main Authors: Yang, Yu, Wang, An, Wang, Hua, Zhao, Wei-Ting, Sun, Dao-Qiang
Format: Article
Language:English
Subjects:
Algorithms
Enumeration
Evolution
fan graph
generating function
Graphs
Mathematics
Network management systems
Network topologies
subtree
wheel graph
“partitions” of wheel graph
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cited_by cdi_FETCH-LOGICAL-c364t-f054b04be4bd3f1a9f1997dff1f580f485e8e5b60ce000a640e2ca1a53bfec53
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container_issue 5
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container_title Mathematics (Basel)
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creator Yang, Yu
Wang, An
Wang, Hua
Zhao, Wei-Ting
Sun, Dao-Qiang
description 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.
doi_str_mv 10.3390/math7050472
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subjects Algorithms
Enumeration
Evolution
fan graph
generating function
Graphs
Mathematics
Network management systems
Network topologies
subtree
wheel graph
“partitions” of wheel graph
title On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution
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