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

Yu Yang, Long Li, Wenhu Wang and Hua Wang
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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
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

Mathematics, 2020, vol. 9, issue 1, 1-29

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.

Keywords: BC-subtree number index; generating function; multi-fan graph; multi-wheel graph; BC-subtree density (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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