Conjugated tricyclic graphs with maximum variable sum exdeg index

Muhammad Rizwan; Akhlaq Ahmad Bhatti; Muhammad Javaid; Yilun Shang

doi:10.1016/j.heliyon.2023.e15706

Conjugated tricyclic graphs with maximum variable sum exdeg index

Heliyon. 2023 Apr 27;9(5):e15706. doi: 10.1016/j.heliyon.2023.e15706. eCollection 2023 May.

Authors

Muhammad Rizwan¹, Akhlaq Ahmad Bhatti¹, Muhammad Javaid², Yilun Shang³

Affiliations

¹ Department of Sciences and Humanities, National University of Computer & Emerging Sciences, Lahore campus, Pakistan.
² Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770, Pakistan.
³ Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK.

Abstract

The variable sum exdeg index, initially introduced by Vukicevic (2011) [20] for predicting the octanol water partition co-efficient of certain chemical compounds, is an invariant for a graph G and defined as $S E I_{a} (G) = \sum_{v \in V (G)} (d_{v} a^{d_{v}})$ , where $d_{v}$ is the degree of vertex $v \in V (G)$ , a is a positive real number different from 1. In this paper, we defined sub-collections of tricyclic graphs say $T_{2 m}^{3}, T_{2 m}^{4}, T_{2 m}^{6}$ and $T_{2 m}^{7}$ . The graph with maximum variable sum exdeg index is characterized from each collection given above with perfect matching. Consequently, through a comparison among these extremal graphs, we indicate the graph which contains maximum $S E I_{a}$ -value from $T_{2 m}$ .

Keywords: Conjugated tricyclic graph; Molecular graph; Variable sum exdeg index.