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Badaoui, Mohamad

Applying algebraic and combinatorics techniques to solve graph problems leads to the birthof algebraic and combinatorial graph theory. This thesis deals mainly with a crossroads questbetween the two theories, that is, the problem of constructing infinite families of expandergraphs.From a combinatorial point of view, expander graphs are sparse graph...

Brouwer, Andries E. Cioabă, Sebastian M. Haemers, Willem H. Vermette, Jason R.
Published in
Journal of Algebraic Combinatorics

The simplicial rook graph SR(m,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SR}(m,n)$$\end{document} is the graph of which the vertices are the sequences o...

Chung, T Koolen, J Sano, Y Taniguchi, T

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Ligong, Wang Xueliang, Li Shenggui, Zhang
Published in
Applied Mathematics-A Journal of Chinese Universities

In this paper, some new classes of integral graphs are given in two new ways. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving diophantine equations. Some classes are infinite. The discovery of these classes is a new contribution to the search of such integral graphs.