Spectrum of prism graph and relation with network related quantities

Ali Raza; Mobeen Munir; Tasawar Abbas; Sayed M Eldin; Ilyas Khan; Ali Raza; Mobeen Munir; Tasawar Abbas; Sayed M Eldin; Ilyas Khan

doi:10.3934/math.2023137

AIMS Mathematics

2023, Volume 8, Issue 2: 2634-2647. doi: 10.3934/math.2023137

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Spectrum of prism graph and relation with network related quantities

1.
Department of Mathematics, University of Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan
2.
Department of Mathematics, University of Wah, Wah Cantt 47040, Pakistan
3.
Center of Research, Faculty of Engineering, Future University in Egypt New Cairo 11835, Egypt
4.
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia

Received: 16 August 2022 Revised: 20 October 2022 Accepted: 24 October 2022 Published: 08 November 2022
MSC : 05C10, 05C82, 68R10

Spectra of network related graphs have numerous applications in computer sciences, electrical networks and complex networks to explore structural characterization like stability and strength of these different real-world networks. In present article, our consideration is to compute spectrum based results of generalized prism graph which is well-known planar and polyhedral graph family belongs to the generalized Petersen graphs. Then obtained results are applied to compute some network related quantities like global mean-first passage time, average path length, number of spanning trees, graph energies and spectral radius.
- polyhedral graph,
- spectrum of graph,
- adjacency matrix,
- Laplacian matrix,
- graph energies
Citation: Ali Raza, Mobeen Munir, Tasawar Abbas, Sayed M Eldin, Ilyas Khan. Spectrum of prism graph and relation with network related quantities[J]. AIMS Mathematics, 2023, 8(2): 2634-2647. doi: 10.3934/math.2023137

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Abstract

Spectra of network related graphs have numerous applications in computer sciences, electrical networks and complex networks to explore structural characterization like stability and strength of these different real-world networks. In present article, our consideration is to compute spectrum based results of generalized prism graph which is well-known planar and polyhedral graph family belongs to the generalized Petersen graphs. Then obtained results are applied to compute some network related quantities like global mean-first passage time, average path length, number of spanning trees, graph energies and spectral radius.

References

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