Ioan Tomescu

93

2

2025

567-574

In this paper, we prove that extremal tree of order \( n \) with given independence number \( s\,\, (n/2\leq s\leq n-1) \) having maximum bond incident degree indices \( \mathcal{T}_{f} \) is the spur graph \( S_{n,s} \) if edge-weight symmetric function \( f(x,y) \) satisfies three conditions: \( f(x,y) \) is strictly increasing on \( x \) (or \( y \)); \( f(x,y)-f(x,y-1) \) is increasing on \( x \) (or \( y \)); \( \varphi(x+1,y-1)\geq \varphi(x,y) \) for every \( x, y\geq 2 \), where \( \varphi(x,y)=f(x,y)-f(x-1,y) \).