The largest Laplacian and adjacency indices of complete caterpillars of fixed diameter
DOI:
https://doi.org/10.4067/S0716-09172015000200006Keywords:
Caterpillar, Laplacian matrix, Laplacian index, Adjacency matrix, Index, Spectral radius.Abstract
A complete caterpillar is a caterpillar in which each internal vertex is a quasi-pendent vertex. In this paper, in the class of all complete caterpillars on n vertices and diameter d, the caterpillar attaining the largest Laplacian index is determined. In addition, it is proved that this caterpillar also attains the largest adjacency index.References
[1] D. Cvetkovic, P. Rowlinson, S. K. Simic, An Introduction to the Theory of Graph Spectra, London Mathematical Society, Student Texts 75, Cambridge University Press, (2010).
[2] J.M. Guo, J-Y. Shao, On the spectral radius of trees with fixed diameter, Linear Algebra and its Applications 413, pp. 131—147, (2006).
[3] J.- M. Guo, On the Laplacian spectral radius of trees with fixed diameter, Linear Algebra Appl. 419, pp. 618-629, (2006).
[4] J.- M. Guo, The effect on the Laplacian spectral radius of a graph by adding or grafting edges, Linear Algebra Appl. 413, pp. 59—71, (2006).
[5] O. Rojo, L. Medina, N. Abreu and C. Justel, On the algebraic connectivity of some caterpillars: A sharp upper bound and a total ordering. Linear Algebra and its Applications 432, pp. 586—605, (2010).
[6] O. Rojo, L. Medina, N. Abreu and C. Justel, Extremal algebraic connectivities of certain caterpillar classes and symmetric caterpillars, Electronic Journal of Linear Algebra, Vol. 20, pp. 136-157, (2010).
[7] O. Rojo, L. Medina, Spectra of generalized Bethe trees attached to a path, Linear Algebra and its Applications 430, pp. 483-503, (2009).
[8] O. Rojo, L. Medina, Spectra of weighted compound graphs of generalized Bethe trees, Electronic Journal of Linear Algebra 18, pp. 30-57, (2009).
[9] S. K. Simic, E. M. L. Marzi, F. Belardo, On the index of caterpillars, Discrete Mathematics 308, pp. 324-330, (2008).
[10] R. S. Varga, Matrix Iterative Analysis, Springer Series in Computational Mathematics, Volume 27, (2000).
[2] J.M. Guo, J-Y. Shao, On the spectral radius of trees with fixed diameter, Linear Algebra and its Applications 413, pp. 131—147, (2006).
[3] J.- M. Guo, On the Laplacian spectral radius of trees with fixed diameter, Linear Algebra Appl. 419, pp. 618-629, (2006).
[4] J.- M. Guo, The effect on the Laplacian spectral radius of a graph by adding or grafting edges, Linear Algebra Appl. 413, pp. 59—71, (2006).
[5] O. Rojo, L. Medina, N. Abreu and C. Justel, On the algebraic connectivity of some caterpillars: A sharp upper bound and a total ordering. Linear Algebra and its Applications 432, pp. 586—605, (2010).
[6] O. Rojo, L. Medina, N. Abreu and C. Justel, Extremal algebraic connectivities of certain caterpillar classes and symmetric caterpillars, Electronic Journal of Linear Algebra, Vol. 20, pp. 136-157, (2010).
[7] O. Rojo, L. Medina, Spectra of generalized Bethe trees attached to a path, Linear Algebra and its Applications 430, pp. 483-503, (2009).
[8] O. Rojo, L. Medina, Spectra of weighted compound graphs of generalized Bethe trees, Electronic Journal of Linear Algebra 18, pp. 30-57, (2009).
[9] S. K. Simic, E. M. L. Marzi, F. Belardo, On the index of caterpillars, Discrete Mathematics 308, pp. 324-330, (2008).
[10] R. S. Varga, Matrix Iterative Analysis, Springer Series in Computational Mathematics, Volume 27, (2000).
How to Cite
[1]
N. Abreu, E. Lenes, and Óscar Rojo, “The largest Laplacian and adjacency indices of complete caterpillars of fixed diameter”, Proyecciones (Antofagasta, On line), vol. 34, no. 2, pp. 175-190, 1.
Issue
Section
Artículos
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.