A new method for the sum-edge characteristic polynomials of graphs
DOI:
https://doi.org/10.5269/bspm.47918Abstract
In this paper, the determinant of the sum-edge adjacency matrix of any given graph without loops is calculated by means of an algebraic method using spanning elementary subgraphs and also the coefficients of the corresponding sum-edge characteristic polynomial are determined by means of the elementary subgraphs. Also we gave a formula for the number of smallest odd-sized cycles in a given regular graph.
References
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14. Oz, M. S., Yamac, C., Cangul, I. N., Sum-edge characteristic polynomials of graphs, Journal of Taibah University for Science 13 (1), 193-200, (2019). https://doi.org/10.1080/16583655.2018.1555989
15. Wong, D., Wang, X., Chu, R., Lower bounds of graph energy in terms of matching number, Linear Algebra and its Applications 549, 276-286, (2018). https://doi.org/10.1016/j.laa.2018.03.040
16. Yamac, C., Oz, M. S., Cangul, I. N., Edge Adjacency in Graphs, Proceedings of the Jangjeon Mathematical Society 21 (3), 357-373, (2018).
17. Yamac, C., Oz, M. S., Cangul, I. N., Edge-Zagreb Indices of Graphs, Turkic World of Mathematical Society Journal of Applied and Engineering Mathematics 9 (1), (2019) (preprint).
2. Bapat, R. B., Graphs and Matrices, Springer, New York (2014). https://doi.org/10.1007/978-1-4471-6569-9
3. Biggs, N., Algebraic Graph Theory, Cambridge University Press, Cambridge (1974). https://doi.org/10.1017/CBO9780511608704
4. Brouwer, A. E., Haemers, W. H., Spectra of Graphs, Springer, New York (2012). https://doi.org/10.1007/978-1-4614-1939-6
5. Chung, F. R. K., Spectral Graph Theory, CBMS 92, American Mathematical Society, Rhode Island (2009).
6. Colman, B., Hill, D., Elementary Linear Algebra with Applications, Prentice Hall, New Jersey (2007).
7. Cvetkovic, D. M., Doob, M., Sachs, H., Spectra of Graphs-Theory and Applications, Academic Press, Cambridge (1980).
8. Das, K. C., Gutman, I., On Laplacian energy, Laplacian-energy-like invariant and Kirchhoff index of graphs, Linear Algebra and its Applications 554, 170-184, (2018). https://doi.org/10.1016/j.laa.2018.05.030
9. Das, K. C., Gutman, I., Milovanovic, I., Milovanovic, E., Furtula, B., Degree-based energies of graphs, Linear Algebra and its Applications 554, 185-204, (2018). https://doi.org/10.1016/j.laa.2018.05.027
10. Das, K. C., Mojallal, S. A., Sun, S., On the sum of the k largest eigenvalues of graphs and maximal energy of bipartite graphs, Linear Algebra and its Applications 569, 175-194, (2019). https://doi.org/10.1016/j.laa.2019.01.016
11. Janezic, D., Milicevic, A., Nikolic, S., Trinajstic, N., Graph Theoretical Matrices in Chemistry, CRC Press, Taylor and Francis Group, Florida (2015). https://doi.org/10.1201/b18389
12. Li, X., Shi, Y., Gutman, I., Graph Energy, Springer, New York (2012). https://doi.org/10.1007/978-1-4614-4220-2
13. Nikiforov, V., Remarks on the energy of regular graphs, Linear Algebra and its Applications 508, 133-145, (2016). https://doi.org/10.1016/j.laa.2016.07.007
14. Oz, M. S., Yamac, C., Cangul, I. N., Sum-edge characteristic polynomials of graphs, Journal of Taibah University for Science 13 (1), 193-200, (2019). https://doi.org/10.1080/16583655.2018.1555989
15. Wong, D., Wang, X., Chu, R., Lower bounds of graph energy in terms of matching number, Linear Algebra and its Applications 549, 276-286, (2018). https://doi.org/10.1016/j.laa.2018.03.040
16. Yamac, C., Oz, M. S., Cangul, I. N., Edge Adjacency in Graphs, Proceedings of the Jangjeon Mathematical Society 21 (3), 357-373, (2018).
17. Yamac, C., Oz, M. S., Cangul, I. N., Edge-Zagreb Indices of Graphs, Turkic World of Mathematical Society Journal of Applied and Engineering Mathematics 9 (1), (2019) (preprint).
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2022-02-02
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