Семинар за примењену математику, 12. октобар 2010.

• 11. Октобар, 2010
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Састанак Семинара за примењену математику одржаће се у уторак, 12.10.2010. у 14:15, сала 301ф МИ САНУ.

Предавач: Pavel Hic, Milan Pokorny, Trnava University in Trnava, Slovak Republic

Назив предавања: INTEGRAL TREES, INTEGRAL COMPLETE MULTIPARTITE GRAPHS

Abstract:

INTEGRAL TREES

The lecture deals with integral trees, which are trees whose zeroes of the adjacency matrix are integers. We present the summary of knowledge about integral trees, with special focus on our results. These results involve integral balanced rooted trees of odd and even diameters, integral balanced rooted trees of diameters 6, 8, and 10, and integral trees of diameter 7. The terms divisor and co-divisor are presented as they play a significant role in our research. At the end chosen open problems are presented.

INTEGRAL COMPLETE MULTIPARTITE GRAPHS

The lecture deals with integral complete multipartite graphs. We present the summary of knowledge about these graphs, with special focus on our results. The presented results involve necessary and sufficient conditions for multipartite graphs to be integral, with special focus on 3-partite, 4-partite, 5-partite, and 6-partite graphs. At the end chosen open problems are presented.