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On the Distance and Distance Signless Laplacian Spectral Radii of Tricyclic Graphs

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Abstract

In this paper, we first obtain the second lower bound on Wiener index for tricyclic graphs. As applications, those graphs with the first four minimum distance (resp. distance signless Laplacian) spectral radius among tricyclic graphs are characterized.

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References

  1. Bollobás, B.: Morden Graph Theory. Springer, Berlin (1998)

    Google Scholar 

  2. Aouchiche, M., Hansen, P.: Two Laplacians for the distance matrix of a graph. Linear Algebra Appl. 439, 21–33 (2013)

    Article  MathSciNet  Google Scholar 

  3. Graham, R.L., Pollack, H.O.: On the addressing problem for loop switching. Bell Syst. Tech. J. 50, 2495–2519 (1971)

    Article  MathSciNet  Google Scholar 

  4. Graham, R.L., Lovász, L.: Distance matrix polynomials of trees. Adv. Math. 29, 60–88 (1978)

    Article  MathSciNet  Google Scholar 

  5. Stevanović, D., IIić, A.: Distance spectral radius of trees with fixed maximum degree. Electron. J. Linear Algebra 20, 168–179 (2010)

    Article  MathSciNet  Google Scholar 

  6. Yu, G., Wu, Y., Zhang, Y., Shu, J.: Some graft transformations and its application on a distance spectrum. Discret. Math. 311, 2117–2123 (2011)

    Article  MathSciNet  Google Scholar 

  7. Paul, S.: On the maximal distance spectral radius in a class of bicyclic graphs. Discret. Math. Algorithms Appl. 4, 1250061 (2012)

    Article  MathSciNet  Google Scholar 

  8. Bose, S.S., Nath, M., Paul, S.: On the maximal distance spectral radius of graphs without a pendent vertex. Linear Algebra Appl. 438, 4260–4278 (2013)

    Article  MathSciNet  Google Scholar 

  9. Nath, M., Paul, S.: On the distance spectral radius of bipartite graphs. Linear Algebra Appl. 436, 1285–1296 (2012)

    Article  MathSciNet  Google Scholar 

  10. Nath, M., Paul, S.: On the distance spectral radius of trees. Linear Multilinear Algebra 61, 847–855 (2013)

    Article  MathSciNet  Google Scholar 

  11. Zhou, B., Ilić, A.: On distance spectral radius and distance energy of graphs. MATCH Commun. Math. Comput. Chem. 64, 261–280 (2010)

    MathSciNet  MATH  Google Scholar 

  12. Xing, R., Zhou, B., Li, J.: On the distance signless Laplacian spectral radius of graphs. Linear Multilinear Algebra 62, 1377–1387 (2014)

    Article  MathSciNet  Google Scholar 

  13. Xing, R., Zhou, B.: On the distance and distance signless Laplacian spectral radii of bicyclic graphs. Linear Algebra Appl. 439, 3955–3963 (2013)

    Article  MathSciNet  Google Scholar 

  14. Aouchiche, M., Hansen, P.: On the distance signless Laplacian of a graph. Linear Multilinear Algebra 64(6), 1113–1123 (2016)

    Article  MathSciNet  Google Scholar 

  15. Das, K.C.: Proof of conjectures on the distance signless Laplacian eigenvalues of graphs. Linear Algebra Appl. 467, 100–115 (2015)

    Article  MathSciNet  Google Scholar 

  16. Lin, H., Lu, X.: Bounds on the distance signless Laplacian spectral radius in terms of clique number. Linear Multilinear Algebra 63(9), 1750–1759 (2015)

    Article  MathSciNet  Google Scholar 

  17. Li, S., Li, X., Zhu, Z.: On tricyclic graphs with minimal energy. MATCH Commun. Math. Comput. Chem. 59, 397–419 (2008)

    MathSciNet  MATH  Google Scholar 

  18. Wang, D., Tan, S., Zhu, L.: On the lower and upper bounds for different indices of tricyclic graphs. J. Appl. Math. Comput. 51, 1–11 (2016)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to express sincere gratitude to the editor and the reviewers for helpful comments in improving the quality of the original manuscript.

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Correspondence to Zhongxun Zhu.

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Communicated by Sanming Zhou.

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This Research is supported by the Special Fund for Basic Scientific Research of Central Colleges, South-Central University for Nationalities (CZY18032).

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Zhu, Z., Zou, X. & Hong, Y. On the Distance and Distance Signless Laplacian Spectral Radii of Tricyclic Graphs. Bull. Malays. Math. Sci. Soc. 43, 2587–2604 (2020). https://doi.org/10.1007/s40840-019-00824-7

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  • DOI: https://doi.org/10.1007/s40840-019-00824-7

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