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, multiwheel (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.
| Original language | English |
|---|---|
| Article number | 36 |
| Pages (from-to) | 1-29 |
| Number of pages | 29 |
| Journal | Mathematics |
| Volume | 9 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2021 |
Keywords
- BC-subtree density
- BC-subtree number index
- Generating function
- Multi-fan graph
- Multi-wheel graph