On Trees with Greatest F-Invariant Using Edge Swapping Operations

Wenhu Wang; Adnan Aslam; Muhammad Ahsan Binyamin; Salma Kanwal; Iqra Irshad

doi:10.1155/2022/8291974

On Trees with Greatest F-Invariant Using Edge Swapping Operations

Comput Intell Neurosci. 2022 Jun 28:2022:8291974. doi: 10.1155/2022/8291974. eCollection 2022.

Authors

Wenhu Wang^{1

2

3}, Adnan Aslam⁴, Muhammad Ahsan Binyamin⁵, Salma Kanwal⁶, Iqra Irshad⁴

Affiliations

¹ School of Software, Pingdingshan University, Pingdingshan, Henan 467000, China.
² International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric Particulate Matter PM2.5, Pingdingshan, Henan 467000, China.
³ College of Computing and Information Technologies, National University, Manila PH1008, Philippines.
⁴ University of Engineering and Technology, Lahore(RCET), Pakistan.
⁵ Department of Mathematics, GC University Faisalabad, Pakistan.
⁶ Department of Mathematics, Lahore College for Women University, Lahore, Pakistan.

Abstract

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.

MeSH terms

Trees*