Leap eccentric connectivity index in graphs with universal vertices

•A large number of topological indices (alias graph invariants) have been defined in mathematical chemistry with the aim of modelling chemical phenomena.•Our goal is to investigate the extremal values of the Leap eccentric connectivity index (LECI) of graphs containing cut vertices.•We prove an upper bound on LECI for trees of a given order and diameter, and determine the extremal trees.•We determine trees with maximum LECI among all trees of a given order. For a graph X, the leap eccentric connectivity index (LECI) is ∑x∈V(X)d2(x,X)ε(x,X), where d2(x,X) is the 2-distance degree and ε(x,X) the eccentricity of x. We establish a lower and an upper bound for the LECI of X in terms of its order and the number of universal vertices, and identify the extremal graphs. We prove an upper bound on the index for trees of a given order and diameter, and determine the extremal trees. We also determine trees with maximum LECI among all trees of a given order.