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On BC-Subtrees in Multi-Fan and Multi-Wheel Graphs

Author

Listed:
  • Yu Yang

    (School of Computer Science, Henan Province Key Laboratory of Germplasm Innovation and Utilization of Eco-economic Woody Plant, Pingdingshan University, Pingdingshan 467000, China)

  • Long Li

    (School of Computer Science, Henan Province Key Laboratory of Germplasm Innovation and Utilization of Eco-economic Woody Plant, Pingdingshan University, Pingdingshan 467000, China
    College of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, China)

  • Wenhu Wang

    (School of Computer Science, Henan Province Key Laboratory of Germplasm Innovation and Utilization of Eco-economic Woody Plant, Pingdingshan University, Pingdingshan 467000, China)

  • Hua Wang

    (Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA)

Abstract

The BC-subtree (a subtree in which any two leaves are at even distance apart) number index is the total number of non-empty BC-subtrees of a graph, and is defined as a counting-based topological index that incorporates the leaf distance constraint. In this paper, we provide recursive formulas for computing the BC-subtree generating functions of multi-fan and multi-wheel graphs. As an application, we obtain the BC-subtree numbers of multi-fan graphs, r multi-fan graphs, multi-wheel (wheel) graphs, and discuss the change of the BC-subtree numbers between different multi-fan or multi-wheel graphs. We also consider the behavior of the BC-subtree number in these structures through the study of extremal problems and BC-subtree density. Our study offers a new perspective on understanding new structural properties of cyclic graphs.

Suggested Citation

  • Yu Yang & Long Li & Wenhu Wang & Hua Wang, 2020. "On BC-Subtrees in Multi-Fan and Multi-Wheel Graphs," Mathematics, MDPI, vol. 9(1), pages 1-29, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:36-:d:468403
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    References listed on IDEAS

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