Polarne dekompozije (Seminar DM)

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Polar decompositions of configurations and exceptional configurations

Arjana Žitnik, UL FMF in IMFM

Torek, 6. 4. 2010 od 10-12, Plemljev seminar, Jadranska 19

Adjacency matrix A(G) of a k-regular graph G can be considered as an incidence matrix of a symmetric combinatorial configuration. We give a necessary and sufficient condition for A(G) to be an incidence matrix of some connected self-polar configuration. Furthermore, the Levi graph of such a configuration is isomorphic to the Kronecker cover of G.

We introduce the notion of polar decomposition of a self-polar combinatorial configuration. As a consequence of the obtained results we show that non-isomorphic graphs may share a common Kronecker cover, which, in turn, implies that the adjacency matrices of these graphs produce isomorphic combinatorial configurations.

Finally, we call a symmetric combinatorial configuration "exceptional" if exactly all the points that are not incident to a given point, lie on the same line. The configuration graph of such a configuration solves an interesting graph equation. We show that there are only a few exceptional configurations.

Glej tudi/See also

Seminar za diskretno matematiko

Osebna orodja