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eigenvalue; Laplacian index; algebraic connectivity; semi-regular graph; regular graph; Hamiltonian graph; planar graph

References:

[1] Bonday, J. A., Murty, U. S. R.: **Graph Theory with Applications**. Macmillan London (1976).

[2] Cvetkovic, D. M., Doob, M., Sachs, H.: **Spectra of Graphs. Theory and Applications**. VEB Deutscher Verlag der Wissenschaften Berlin (1980).

[3] Fiedler, M.: **Algebraic connectivity of graphs**. Czechoslovak Math. J. 23 (1973), 298-305. MR 0318007 | Zbl 0265.05119

[4] Gracssi, R.: **Relevant inequalities in graph connectivity**. Arch. Ineqal. Appl. 2 (2004), 183-198. MR 2106953

[5] Gutman, I.: **The star is the tree with greatest Laplacian eignvalue**. Kragujevac J. Math. 24 (2002), 61-65. MR 1947659

[6] Haemers, W. H.: **Interlacing eigenvalues and graphs**. Linear Algebra Appl. 227-228 (1995), 593-616. MR 1344588 | Zbl 0831.05044

[8] Merris, R.: **Laplacian matrices of graphs: A survey**. Linear Algebra Appl. 197-198 (1994), 143-176. MR 1275613 | Zbl 0802.05053