The second and third Hankel determinants for starlike and convex functions associated with Three-Leaf function.

In this paper, we give sharp bounds of the Hankel determinant H 2 ( 3 ) ( f ) for the coefficients of functions in the class of starlike functions related to a domain that is like three leaves. We also give sharp bounds for the Hankel determinants H 3 ( 1 ) ( f ) and H 2 ( 3 ) ( f ) for the coefficients of functions in the class of convex functions related to the three-leaf-like domain.

On Trees with Greatest F-Invariant Using Edge Swapping Operations.

The F-index of a graph Q is defined as F(Q)=∑ t∈V(Q)(d t )3. In this paper, we use edge swapping transformations to find the extremal value of the F-index among the class of trees with given order, pendent vertices, and diameter. We determine the trees with given order, pendent vertices, and diameter having the greatest F-index value. Also, the first five maximum values of F index among the class of trees with given diameter are determined.