@article {26571,
	title = {Nodal domains of eigenvectors for 1-Laplacian on graphs},
	journal = {Advances in Mathematics},
	volume = {308},
	year = {2017},
	pages = {529-574},
	abstract = {The eigenvectors for graph 1-Laplacian possess some sort of localization property: On one hand, the characteristic function on any nodal domain of an eigenvector is again an eigenvector with the same eigenvalue; on the other hand, one can pack up an eigenvector for a new graph by several fundamental eigencomponents and modules with the same eigenvalue via few special techniques. The Courant nodal domain theorem for graphs is extended to graph 1-Laplacian for strong nodal domains, but for weak nodal domains it is false. The notion of algebraic multiplicity is introduced in order to provide a more precise estimate of the number of independent eigenvectors. A positive answer is given to a question raised in Chang (2016) [3], to confirm that the critical values obtained by the minimax principle may not cover all eigenvalues of graph 1-Laplacian.},
	url = {http://dx.doi.org/10.1016/j.aim.2016.12.020},
	author = {K.-C. Chang and Sihong Shao and Dong Zhang}
}
