On Trees with Greatest F − Invariant Using Edge Swapping Operations

Abstract

The $F$ -index of a graph $Q$ is defined as $F\left(Q\right)={\displaystyle {\sum }_{t\in V\left(Q\right)}{\left(d_t\right)}^3}$ . 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.