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Current Organic Synthesis

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ISSN (Print): 1570-1794
ISSN (Online): 1875-6271

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Research Article

Computing the Energy of Certain Graphs based on Vertex Status

Author(s): Asim Khurshid and Muhammad Salman*

Volume 21, Issue 3, 2024

Published on: 01 September, 2023

Page: [274 - 285] Pages: 12

DOI: 10.2174/1570179420666230811124140

Price: $65

Abstract

Background: The concept of Hückel molecular orbital theory is used to compute the graph energy numerically and graphically on the base of the status of a vertex.

Objective: Our aim is to explore the graph energy of various graph families on the base of the status adjacency matrix and its Laplacian version.

Methods: We opt for the technique of finding eigenvalues of adjacency and Laplacian matrices constructed on the base of the status of vertices.

Results: We explore the exact status sum and Laplacian status sum energies of a complete graph, complete bipartite graph, star graphs, bistar graphs, barbell graphs and graphs of two thorny rings. We also compared the obtained results of energy numerically and graphically.

Conclusion: In this article, we extended the study of graph spectrum and energy by introducing the new concept of the status sum adjacency matrix and the Laplacian status sum adjacency matrix of a graph. We investigated and visualized these newly defined spectrums and energies of well-known graphs, such as complete graphs, complete bi-graphs, star graphs, friendship graphs, bistar graphs, barbell graphs, and thorny graphs with 3 and 4 cycles.

Keywords: Distance, status of a vertex, adjacency matrix, laplacian matrix, energy, graphs.

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