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all-bib.bib
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@article{VANDAM1995139,
title = "Honoring J.J.Seidel Regular graphs with four eigenvalues",
journal = "Linear Algebra and its Applications",
volume = "226",
number = "",
pages = "139 - 162",
year = "1995",
note = "",
issn = "0024-3795",
doi = "http://dx.doi.org/10.1016/0024-3795(94)00346-F",
url = "http://www.sciencedirect.com/science/article/pii/002437959400346F",
author = "Edwin R. van Dam",
abstract = "We study the connected regular graphs with four distinct eigenvalues. Properties and feasibility conditions of the eigenvalues are found. Several examples, constructions and characterizations are given, as well as some uniqueness and nonexistence results."
}
@inproceedings{mihail1989conductance,
title={Conductance and convergence of Markov chains-a combinatorial treatment of expanders},
author={Mihail, M},
booktitle={Foundations of Computer Science, 1989., 30th Annual Symposium on},
pages={526--531},
organization={IEEE}
}
@article{hogben2005spectral,
title={Spectral graph theory and the inverse eigenvalue problem of a graph},
author={Hogben, Leslie},
journal={Electronic Journal of Linear Algebra},
volume={14},
number={1},
pages={3},
year={2005}
}
@article{de1998multiplicities,
title={Multiplicities of eigenvalues and tree-width of graphs},
author={de Verdi{\`e}re, Yves Colin},
journal={Journal of Combinatorial Theory, Series B},
volume={74},
number={2},
pages={121--146},
year={1998},
publisher={Elsevier}
}
@article{de2007old,
title={Old and new results on algebraic connectivity of graphs},
author={De Abreu, Nair Maria Maia},
journal={Linear algebra and its applications},
volume={423},
number={1},
pages={53--73},
year={2007},
publisher={Elsevier}
}
@article{fiedler1973algebraic,
title={Algebraic connectivity of graphs},
author={Fiedler, Miroslav},
journal={Czechoslovak mathematical journal},
volume={23},
number={2},
pages={298--305},
year={1973},
publisher={Institute of Mathematics, Academy of Sciences of the Czech Republic}
}
@article{fiedler1975property,
title={A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory},
author={Fiedler, Miroslav},
journal={Czechoslovak Mathematical Journal},
volume={25},
number={4},
pages={619--633},
year={1975},
publisher={Institute of Mathematics, Academy of Sciences of the Czech Republic}
}
@article{Hong2004281,
title = "Tree-width, clique-minors, and eigenvalues ",
journal = "Discrete Mathematics ",
volume = "274",
number = "1–3",
pages = "281 - 287",
year = "2004",
note = "",
issn = "0012-365X",
doi = "http://dx.doi.org/10.1016/S0012-365X(03)00199-7",
url = "http://www.sciencedirect.com/science/article/pii/S0012365X03001997",
author = "Yuan Hong",
keywords = "Graph minor",
keywords = "Tree-width",
keywords = "Surface",
keywords = "Eigenvalue ",
abstract = "Let G be a simple graph with n vertices and tw(G) be the tree-width of G. Let ρ(G) be the spectral radius of G and λ(G) be the smallest eigenvalue of G. The join G∇H of disjoint graphs of G and H is the graph obtained from G+H by joining each vertex of G to each vertex of H. In this paper, several results which are concerned with tree-width, clique-minors, and eigenvalues of graphs are given. In particular, we have (1) If G is \{K5\} minor-free graph, thenρ(G)⩽1+3n−8,where equality holds if and only if G is isomorphic to K3∇(n−3)K1. (2) If G is \{K5\} minor-free graph with n⩾5 vertices, thenλ(G)⩾−3n−9,where equality holds if and only if G is isomorphic to K3,n−3. "
}