Extremal problems on the Atom-bond sum-connectivity indices of trees with given matching number or domination number

The atom-bond sum-connectivity (ABS) index of a graph is a variant from some famous chemical topological indices such as the Randić index, the sum-connectivity index and the atom-bond connectivity index. The research on its extremal problems of a graph has much theoretical value and application background. Let T_n,m and T(n,γ) be the sets of all trees on n vertices with given matching number m and given dominating number γ, respectively. In this paper, we firstly determine the sharp upper bound of the ABS index among T_n,m and characterize the corresponding extremal graph. Secondly, we determine the sharp upper and lower bounds of the ABS index among T(n,γ) by using the bridge of the matching theory. Finally, the corresponding topological structures of their extremal graphs are characterized, respectively.