Elliptic Sombor index of trees and unicyclic graphs

Let G = G(V, E) be a simple connected graph with vertex set V and edge set E. The elliptic Sombor index of G is defined as, where d(u) denotes the degree of vertex u.In this paper, the maximal value of the elliptic Sombor index of trees with a given diameter or matching number or number of pendent vertices is determined.The extremal values of the elliptic Sombor index of unicyclic graphs are also found.Furthermore, those trees and unicyclic graphs that achieve the obtained extremal values are characterized.