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Conjugated tricyclic graphs with maximum variable sum exdeg index

2023; Elsevier BV; Volume: 9; Issue: 5 Linguagem: Inglês

10.1016/j.heliyon.2023.e15706

2405-8440

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

Graph Labeling and Dimension Problems

The variable sum exdeg index, initially introduced by Vukicevic (2011) [[20]Vukicevic D. Bond additive modelling 5. Mathematical properties of the variable sum exdeg index.Croat. Chem. Acta. 2011; 84: 93-101https://doi.org/10.5562/cca1667Crossref Google Scholar] for predicting the octanol water partition co-efficient of certain chemical compounds, is an invariant for a graph G and defined as SEIa(G)=∑v∈V(G)(dvadv), where dv is the degree of vertex v∈V(G), a is a positive real number different from 1. In this paper, we defined sub-collections of tricyclic graphs say T2m3,T2m4,T2m6 and T2m7. 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 SEIa-value from T2m.