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.