THE NONLINEAR PROGRAMMING APPROACH TO THE SOMBOR INDEX

In this paper, a nonlinear mathematical programming problem is considered and solved using quadratic constraints in the optimization model. We find extremal graphs or obtain precise bounds for the Sombor index and identify extremal graph structures for the set of connected simple graphs of class G(k, n) of order n with minimum degree k when the number nk of vertices with degree k is nk = n-k+t, where ۰ ≤ t ≤ k and ۱ ≤ k ≤ n − ۱. Specifically, we aim to prove that for nk ≥ n − k, where ۱ ≤ k ≤ n − ۱, the graph G attains the maximum Sombor index for the graphs and the minimum Sombor index value for k-regular graphs.

کلیدواژه ها:

Sombor index ، extremal graphs ، nonlinear programming problem