Calculation and comparison of energy and energy based on Mostar index of the double-star graph and its line graph

Rajabinejad, Zohreh

doi:10.47974/JDMSC-2246

Open Access Research Article

Calculation and comparison of energy and energy based on Mostar index of the double-star graph and its line graph

Zohreh Rajabinejadzohreh_rajabinejad@semnan.ac.irDepartment of MathematicsFaculty of Mathematics, Statistics and Computer ScienceSemnan UniversitySemnan, P. O. Box 35195-363, Iran0009-0008-0379-0120View full profile →

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pp. 1585–1594Vol. 29Issue 4April 2026DOI: 10.47974/JDMSC-2246 Crossmark XML

Received:: 07 Aug 2024
Published Online:: 15 Sep 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2246
Pages:: 1585–1594

Abstract

The double-star line graph is a graph built from two complete graphs of order a+1 that share a common vertex, for every positive integer a ≥ 1. In this article, we investigate concepts of energy and energy based on the Mostar index of Dsa and LDsa graphs and provide a low bound for energies. We obtain general formulas for energies of Dsa, LDsa, MoDsa, and MoLDsa. This study obtains general formulas for the Mostar energy and energy of Dsa and LDsa. Using these formulas does not require calculating eigenvalues, and we show that the energy of these graphs only depends on a, the Number of pendeng edges. We compare energies and find relationships between them. Also, we determine the highest and lowest energy. We display the obtained results, numerically and graphically and compare energies graphically.

Keywords

Double-star graph Double-star line graph Characteristic polynomial Adjacency matrix Eigenvalue Spectrum Graph energy Mostar index

Subject Classifications

05C9005C0905C3105C92

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