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Roy, Roshni, K A, Germina, K, Shahul. (1402). Normalized distance Laplacian matrices for signed graphs. , 8(3), 445-456. doi: 10.22049/cco.2022.27514.1282
Roshni T. Roy; Germina K A; Shahul Hameed K. "Normalized distance Laplacian matrices for signed graphs". , 8, 3, 1402, 445-456. doi: 10.22049/cco.2022.27514.1282
Roy, Roshni, K A, Germina, K, Shahul. (1402). 'Normalized distance Laplacian matrices for signed graphs', , 8(3), pp. 445-456. doi: 10.22049/cco.2022.27514.1282
Roy, Roshni, K A, Germina, K, Shahul. Normalized distance Laplacian matrices for signed graphs. , 1402; 8(3): 445-456. doi: 10.22049/cco.2022.27514.1282

Normalized distance Laplacian matrices for signed graphs

Communications in Combinatorics and Optimization
مقاله 1، دوره 8، شماره 3، آذر 2023، صفحه 445-456    اصل مقاله (405.91 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2022.27514.1282
نویسندگان
Roshni T. Roy* 1؛ Germina K A1؛ Shahul Hameed K2
1Department of Mathematics, Central University of Kerala, Kasaragod - 671316, Kerala, India
2Department of Mathematics, K M M Government\ Women's College, Kannur - 670004, Kerala, India
چکیده
In this paper, we introduce the notion of normalized distance Laplacian matrices for signed graphs corresponding to the two signed distances defined for signed graphs. We characterize balance in signed graphs using these matrices and compare the normalized distance Laplacian spectral radius of signed graphs with that of all-negative signed graphs. Also we characterize the signed graphs having maximum normalized distance Laplacian spectral radius.
کلیدواژه‌ها
Signed graphs؛ Weighted signed graphs؛ Normalized distance Laplacian matrix؛ Normalized distance Laplacian spectrum
مراجع
[1] F. Chung, Spectral Graph Theory, AMS, Providence, RI, 1997.

[2] S. Hameed K, T.V. Shijin, P. Soorya, K.A. Germina, and T. Zaslavsky, Signed distance in signed graphs, Linear Algebra Appl. 608 (2021), 236–247.

[3] F. Harary, Graph Theory, Addison Wesley, Reading, Mass., 1969.

[4] Y. Hou, J. Li, and Y. Pan, On the Laplacian eigenvalues of signed graphs, Linear Multilinear Alg. 51 (2003), no. 1, 21–30.

[5] H.-h. Li and J.-sh. Li, Note on the normalized Laplacian eigenvalues of signed graphs, Australas. J. Combin. 44 (2009), 153–162.

[6] H.S. Li and H.H. Li, A note on the least (normalized) Laplacian eigenvalue of signed graphs, Tamkang J. Math. 47 (2016), no. 3, 271–278.

[7] S. Pirzada and S. Khan, On distance Laplacian spectral radius and chromatic number of graphs, Linear Algebra Appl. 625 (2021), 44–54.

[8] C. Reinhart, The normalized distance Laplacian, Special Matrices 9 (2021), no. 1, 1–18.

[9] R.T. Roy, K.A. Germina, S. Hameed K, and T. Zaslavsky, Signed distance Laplacian matrices for signed graphs, (2020), communicated.

[10] T. Zaslavsky, Signed graphs, Discrete Appl. Math. 4 (1982), no. 1, 47–74.

 

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