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Conjugated tricyclic graphs with maximum variable sum exdeg index.

Muhammad Rizwan1, Akhlaq Ahmad Bhatti1, Muhammad Javaid2

  • 1Department of Sciences and Humanities, National University of Computer & Emerging Sciences, Lahore campus, Pakistan.

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|June 12, 2023
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Summary
This summary is machine-generated.

This study characterizes graphs with maximum variable sum exdeg index within specific tricyclic graph collections. It identifies the extremal graph with the highest index value among these collections.

Keywords:
Conjugated tricyclic graphMolecular graphVariable sum exdeg index

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Area of Science:

  • Graph Theory
  • Chemical Informatics

Background:

  • The variable sum exdeg index, introduced by Vukicevic (2011), predicts octanol water partition coefficients.
  • This index is a graph invariant defined using vertex degrees and a parameter 'a'.

Purpose of the Study:

  • To define and analyze sub-collections of tricyclic graphs.
  • To characterize the graph with the maximum variable sum exdeg index within these collections.
  • To compare extremal graphs and identify the one with the highest index value.

Main Methods:

  • Definition of specific sub-collections of tricyclic graphs.
  • Characterization of graphs with maximum variable sum exdeg index, particularly those with perfect matchings.
  • Comparative analysis of identified extremal graphs.

Main Results:

  • Identification of graphs possessing the maximum variable sum exdeg index within the defined tricyclic graph sub-collections.
  • Characterization of these extremal graphs, with emphasis on those featuring perfect matchings.
  • Determination of the graph with the highest variable sum exdeg index through comparison.

Conclusions:

  • The study successfully characterizes extremal graphs within specific tricyclic collections based on the variable sum exdeg index.
  • The findings provide insights into the behavior of this index in relation to graph structure and perfect matchings.
  • A comparative analysis identified the graph with the maximum index value among the studied collections.