论文信息 - LARGEST EIGENVALUES OF THE DISCRETE P-LAPLACIAN OF TREES WITH DEGREE SEQUENCES ∗

LARGEST EIGENVALUES OF THE DISCRETE P-LAPLACIAN OF TREES WITH DEGREE SEQUENCES ∗

Trees that have greatest maximum p-Laplacian eigenvalue among all trees with a given degree sequence are characterized. It is shown that such extremal trees can be obtained by breadth-first search where the vertex degrees are non-increasing. These trees are uniquely determined up to isomorphism. Moreover, their structure does not depend on p.

[1] Xiao-Dong Zhang,et al. The Laplacian spectral radii of trees with degree sequences , 2008, Discret. Math..

[2] Bernhard Schölkopf,et al. Regularization on Discrete Spaces , 2005, DAGM-Symposium.

[3] Regina Tyshkevich,et al. Lectures on Graph Theory , 1994 .

[4] J. Leydold,et al. Largest Laplacian Eigenvalue and Degree Sequences of Trees , 2008, 0804.2776.

[5] Saïd Amghibech. Bounds for the largest p-Laplacian eigenvalue for graphs , 2006, Discret. Math..

[6] R. Merris. Laplacian matrices of graphs: a survey , 1994 .

[7] M. Yamasaki. Ideal boundary limit of discrete Dirichlet functions , 1986 .

[8] Saïd Amghibech,et al. On the discrete version of Picone's identity , 2008, Discret. Appl. Math..

[9] Saïd Amghibech,et al. Eigenvalues of the Discrete p-Laplacian for Graphs , 2003, Ars Comb..

[10] Claude Berge,et al. Lectures on graph theory , 1967 .

[11] Abderrahim Elmoataz,et al. Graph regularization for color image processing , 2007, Comput. Vis. Image Underst..

[12] Hiroshi Takeuchi. The spectrum of the $p$-Laplacian and $p$-harmonic morphisms on graphs , 2003 .