Maximum bond incident degree indices for trees and unicyclic graphs with given maximum degree

The bond incident degree (BID) index T f ( G ) of a connected graph G with edge-weight function f ( x , y ) is defined as T f ( G ) = ∑ v i v j ∈ E ( G ) f ( d ( v i ) , d ( v j ) ) , where f ( x , y ) > 0 is a symmetric real function with x ≥ 1 and y ≥ 1 and d ( u ) is the degree of vertex u in G . In this paper, we find extremal trees and unicyclic graphs of order n with given maximum degree having maximum bond incident degree index T f if edge-weight symmetric function f ( x , y ) satisfies five conditions. These conditions are fulfilled by sum-connectivity index, general sum-connectivity index, modified Sombor index and harmonic index.