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Some bounds on the distance-sum-connectivity matrix.

Gülistan Kaya Gök¹

¹Department of Mathematics Education, Hakkari University, Hakkari, Turkey.

Journal of Inequalities and Applications

|August 24, 2018

Summary

This study introduces new inequalities for graph energy, incidence energy, and matching energy using the distance-sum-connectivity matrix. These findings relate graph properties like edges, vertices, and degrees to spectral graph theory concepts.

Area of Science:

Graph theory
Spectral graph theory
Mathematical chemistry

Background:

The distance-sum-connectivity matrix provides a novel way to represent graph structures.
Understanding graph energies (graph energy, incidence energy, matching energy) is crucial in various chemical and mathematical applications.

Purpose of the Study:

To derive new inequalities involving graph eigenvalues, graph energy, graph incidence energy, and matching energy.
To establish relationships between these energies and fundamental graph properties such as edges, vertices, and degrees.

Main Methods:

Utilizing the definition of the distance-sum-connectivity matrix.
Applying mathematical and spectral graph theory techniques to derive inequalities.

Main Results:

Keywords:

Bounds Distance-sum-connectivity matrix

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New inequalities connecting graph energies and eigenvalues with graph parameters (edges, vertices, degrees) were established.
The distance-sum-connectivity matrix was shown to be a useful tool for deriving these spectral graph properties.

Conclusions:

The research expands the theoretical understanding of graph energies and their relationship to graph structure.
The derived inequalities offer new analytical tools for studying graph properties in spectral graph theory.