Article ID: MTJPAM-D-24-00065

Title: Spectra and energy of the vertex labeled complement of graphs

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00065; Volume 6 / Issue 3 / Year 2024, Pages 484-491

Document Type: Research Paper

Author(s): ‪Indrani Yambari Radha Lakshmi ^a , Kavita Shivanna Permi ^b , Madhwesha Moudgalya Ravi ^c , Ismail Naci Cangul ^d

^aDepartment of Mathematics, Presidency University, Bangalore 560064, India — Department of Mathematics, Nrupathunga University (aka Government Science College), Bangalore 560001 India

^bDepartment of Mathematics, Presidency University, Bangalore 560064, India

^cDepartment of Mathematics, The Oxford College of Engineering, Bangalore 560068, India

^dBursa Uludag University, Department of Mathematics, Bursa 16059, Turkey

Received: 14 May 2024, Accepted: 6 February 2025, Published: 11 July 2025

Corresponding Author: Ismail Naci Cangul (Email address: cangul@uludag.edu.tr)

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Abstract

For any graph, the sum of the absolute values of the eigenvalues of the adjacency matrix is known as the energy of graph. In this paper, we find the spectrum and energy of vertex labeled complement of distinct graphs along with their bounds and extend it to three applications for the complements of some alkanes.

Keywords: Vertex labeled graph, complement of a graph, spectrum, energy, alkanes

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