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

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

^*Corresponding author for this work

Computer and Information Sciences

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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 SEI_a(G)=∑_v∈V(G)(d_va^d_v), where d_v 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 T_2m³,T_2m⁴,T_2m⁶ and T_2m⁷. 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 SEI_a-value from T_2m.

Original language	English
Article number	e15706
Pages (from-to)	1-11
Number of pages	11
Journal	Heliyon
Volume	9
Issue number	5
Early online date	27 Apr 2023
DOIs	https://doi.org/10.1016/j.heliyon.2023.e15706
Publication status	Published - 1 May 2023

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1-s2.0-S2405844023029134-mainFinal published version, 506 KBLicence: CC BY-NC-ND

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title = "Conjugated tricyclic graphs with maximum variable sum exdeg index",

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 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.",

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AU - Rizwan, Muhammad

AU - Bhatti, Akhlaq Ahmad

AU - Javaid, Muhammad

AU - Shang, Yilun

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AB - 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 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.

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Conjugated tricyclic graphs with maximum variable sum exdeg index

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