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.