On the spectra of a new duplication based corona of graphs

Renny P. Varghese and D. Susha
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 1, Pages 208—220
DOI: 10.7546/nntdm.2021.27.1.208-220
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Authors and affiliations

Renny P. Varghese
Department of Mathematics, Catholicate College
Pathanamthitta, Kerala 689 645, India

D. Susha
Department of Mathematics, Catholicate College
Pathanamthitta, Kerala 689 645, India

Abstract

In this paper we introduce a new corona-type product of graphs namely duplication corresponding corona. Here we mainly determine the adjacency, Laplacian and signless Laplacian spectra of the new graph product. In addition to that, we find out the incidence energy, the number of spanning trees, Kirchhoff index and Laplacian-energy-like invariant of the new graph. Also we discuss some new classes of cospectral graphs.

Keywords

  • Spectrum
  • Corona
  • Duplication graph
  • Incidence energy
  • Spanning tree
  • Kirchhoffindex
  • Laplacian-energy-like invariant

2010 Mathematics Subject Classification

  • 05C50
  • 05C76

References

  1. Brouwer, A. E., & Haemers, W. H. (2012).Spectra of Graphs, Springer.
  2. Cvetkovic, D. M., Doob, M., & Sachs, H. (1995). Spectra of Graphs, Theory and Applications, Third edition, Johann Ambrosius Barth, Heidelberg.
  3. Cvetkovic, D. M., Gutman, I. & Simic, S. K. (1978). On self pseudo-inverse graphs, Univ. Beograd Publ. Elektrotehn. Fak., Ser. Mat. Fiz., 602–633, 111–117.
  4. Cvetkovic, D. M., & Simic, S. K. (2009). Towards a spectral theory of graphs based on the signless Laplacian. Publications de l’Institut Mathematique, Nouvelle series, 85(99), 19–33.
  5. Frucht, H., & Harary, F. (1970). On the corona of two graphs. Aequationes Mathematicae, 4, 322–325.
  6. Gopalapillai, I. (2011). The spectrum of neighborhood corona of graphs. Kragujevac Journal of Mathematics, 35, 493–500.
  7. Grone, R., Merris, R., & Sunder, V. S. (1990). The Laplacian spectrum of a graph. SIAM Journal on Matrix Analysis and Applications, 11, 218–238.
  8. Jooyandeh, M., Kiania, D., & Mirzakhaha, M. (2009). Incidence energy of a graph. MATCH Communications in Mathematical and in Computer Chemistry, 62, 561–572.
  9. Klein, D. J., & Randic, M. (1993). Resistance distance. Journal of Mathematical Chemistry,12, 81–95.
  10. Kumar, K. R., & Varghese, R. P. (2017). Spectrum of(k,r)-regular hyper graphs. International Journal of Mathematical Combinatorics, 2, 52–59.
  11. Li, J., Shiu, W. C., & Chang, A. (2010). The number of spanning tree of a graph. Applied Mathematics Letters, 23, 286–290.
  12. Liu, J., & Liu, B. (2008). A Laplacian-energy-like invariant of a graph. MATCH Communications in Mathematical and in Computer Chemistry, 59, 397–413.
  13. McLeman, C., & McNicholas, E. (2011). Spectra of coronae. Linear Algebra and its Applications, 435, 998–1007.
  14. Merris, R. (1994). Laplacian matrices of graphs: A survey. Linear Algebra and its Applications, 197, 143–176.
  15. Sampathkumar, E. (1973). On duplicate graphs. Journal of the Indian Mathematical Society,37, 285–293.
  16. Sarkar, P., De, N., & Pal, A. (2020). Zagreb indices of double join and double corona of graphs based on the total graph. International Journal of Applied and Computational Mathematics, 6, Art. No. 73.
  17. Varghese, R. P., & Susha, D. (2017). Spectrum of some new product of graphs and its applications. Global Journal of Pure and Applied Mathematics, 13(9), 4493–4504.
  18. Varghese, R. P. & Susha, D. (2017). The spectrum of two new corona of graphs and its applications. International Journal of Mathematics And Its Applications, 5(4–C), 395—406.
  19. Varghese, R. P., & Susha, D. (2020). On the normalized Laplacian spectrum of some graphs. Kragujevac Journal of Mathematics, 44(3), 431–442.

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Cite this paper

Varghese, R. P. & Susha, D. (2021). On the spectra of a new duplication based corona of graphs. Notes on Number Theory and Discrete Mathematics, 27(1), 208-220, doi: 10. 7546/nntdm.2021.27.1.208-220.

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