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Laplacian and signless laplacian spectra and energies of multi-step wheels

1 Department of Mathematics and Physics, Anhui Xinhua University, Hefei 230088, China
2 Division of Science and Technology, University of Education, Lahore 54000, Pakistan
3 Department of Mathematics, COMSATS University Islamabad, Vehari campus, Vehari 61100, Pakistan
4 School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China

Special Issues: Computational Materials Science

Energies and spectrum of graphs associated to different linear operators play a significant role in molecular chemistry, polymerisation, pharmacy, computer networking and communication systems. In current article, we compute closed forms of signless Laplacian and Laplacian spectra and energies of multi-step wheel networks Wn,m. These wheel networks are useful in networking and communication, as every node is one hoop neighbour to other. We also present our results for wheel graphs as particular cases. In the end, correlation of these energies on the involved parameters m ≥ 3 and n is given graphically. Present results are the natural generalizations of the already available results in the literature.
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Keywords laplacian matrix; signless laplacian matrix; spectrum; laplacian energy; signless laplacian energy; wheel graphs

Citation: Zheng-Qing Chu, Mobeen Munir, Amina Yousaf, Muhammad Imran Qureshi, Jia-Bao Liu. Laplacian and signless laplacian spectra and energies of multi-step wheels. Mathematical Biosciences and Engineering, 2020, 17(4): 3649-3659. doi: 10.3934/mbe.2020206

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