Maximal bond incident degree index for trees and unicyclic graphs with fixed diameter

The bond incident degree index of $G$ is defined as

$$BID(G)=\sum _{u_1{u}_2\in E(G)}f(d(u_1),d(u_2)),$$

where $f(y,x)=f(x,y)$ is a real-valued function. In this paper, using graph transformation methods, we respectively established the maximum bond incident degree indices of trees and unicyclic graphs with a fixed diameter. As an application of the sufficient conditions, we verified that six bond incident degree indices satisfy such conditions, among which are the newly introduced Euler Sombor index and the computationally complex general Sombor index.