Seminar on Applied Mathematics
Pavel Hic, Milan Pokorny, Trnava University in Trnava, Slovak Republic
INTEGRAL COMPLETE MULTIPARTITE GRAPHS
Abstract1: 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.
Abstract2: 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.
Dusan Savic, Faculty of Organizational Sciences, University in Belgrade
EXTENDED SOFTWARE ARCHITECTURE BASED ON SECURITY PATTERNS
Abstract: One of the major activities in software design is defining software architecture. Before designing software structure and software behavior we have to define its architecture. In this paper we have proposed three-tiered software architecture. This software architecture extends application logic tier with security. We have implemented two important security issues: authentication and authorization processes. These processes are implemented through software patterns. The software patterns have the particular place in the Proposed Software Architecture (PSA). In this paper, we have presented these software patterns and explained why they are important in PSA.
Keywords: software architecture, software patterns, authentication and authorization processes, software development process.
Tatjana Aleksic, Prirodno-matematicki fakultet, Kragujevac
GRAFOVI CIJA JE NAJMANJA KARAKTERISTICNA VREDNOST MINIMALNA
Sadrzaj: Tema predavanja je najmanja karakteristicna vrednost grafova. Bice reci o tome kakvu strukturu imaju povezani grafovi cija je najmanja karakteristicna vrednost minimalna medju grafovima sa fiskiranim brojem cvorova i grana. Specijalno, osvrnucemo se na odredjivanje ovakvih jedinstvenih ekstremalnih grafova u nekim klasama grafova (unciklicni, biciklicni, triciklicni, kaktusi,..