A few properties of the eigenvalues of normalized graph Laplacian
Combinatorics
2014-03-07 v2 Discrete Mathematics
Abstract
Here we have investigated a few properties of the eigenvalues of normalized (geometric) graph Laplacian in different graphs. Preservation of eigenvalue 1 from a particular subgraph to the entire graph, the spectrum of the graph constructed with triangles share a common vertex have been addressed. Further using the number and degrees of common neighbors between vertices some new upper bounds for the largest eigenvalue have been introduced.
Keywords
Cite
@article{arxiv.1210.5091,
title = {A few properties of the eigenvalues of normalized graph Laplacian},
author = {Anirban Banerjee},
journal= {arXiv preprint arXiv:1210.5091},
year = {2014}
}
Comments
This paper has been withdrawn by the author due to a crucial error in equation 17