On Subtree Number Index of Generalized Book Graphs, Fan Graphs, and Wheel Graphs

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Abstract
With generating function and structural analysis, this paper presents the subtree generating functions and the subtree number index of generalized book graphs, generalized fan graphs, and generalized wheel graphs, respectively. As an application, this paper also briefly studies the subtree number index and the asymptotic properties of the subtree densities in regular book graphs, regular fan graphs, and regular wheel graphs. The results provide the basis for studying novel structural properties of the graphs generated by generalized book graphs, fan graphs, and wheel graphs from the perspective of the subtree number index.
Funding Information
  • National Natural Science Foundation of China (61702291, 11801371, 19HASTIT029, 19B110011, 19B630015, PXY-BSQD2017006)
  • Program for Science & Technology Innovation Talents in Universities of Henan Province (61702291, 11801371, 19HASTIT029, 19B110011, 19B630015, PXY-BSQD2017006)
  • Key Research Project in Universities of Henan Province (61702291, 11801371, 19HASTIT029, 19B110011, 19B630015, PXY-BSQD2017006)
  • Pingdingshan University (61702291, 11801371, 19HASTIT029, 19B110011, 19B630015, PXY-BSQD2017006)

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