We give sharp bounds on the Sombor index of chemical trees and characterize the
cases of the equalities. We stated conjectures regarding second maximal chemical trees of order n with respect to Sombor index, when n ≡ 0(mod 3) and n ≡ 1(mod 3).
In this paper, we consider Tower of Hanoi graphs and study their matching properties. Explicit system of recurrences is derived for the matching polynomials of these graphs and their appropriate truncated variants. Consequently, we obtain exact formula for the numbers of maximum matchings in Hanoi graphs using matching polynomials, which is a new approach for old one problem.
We give sharp bounds on the Sombor index of chemical trees and characterize the
cases of the equalities. We stated conjectures regarding second maximal chemical trees of order n with respect to Sombor index, when n ≡ 0(mod 3) and n ≡ 1(mod 3).
