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Graph theory

Miloš Kaličanin

Regional talent center Belgrade II, Belgrade,miloskali@hotmail.com
the road map. After touring the last city we would return
back to Belgrade. Determine the order of the city tours and
1. Introduction returning to the hotel to obtain the shortest path.

To check the results, I used a graph with assigned
The purpose of research is introduction to the graphs using weightiness that I made with the help of graph theory. The
definitions and theorems, as well as setting of the problem results were:
and coming up with a solution in different ways. In this
research I will adduce general characteristics and some
types of graphs, such as Euler's and Hamilton's, which is a
theoretical introduction to the graphs. The practical
application of this knowledge will be reflected in the
analysis and resolution of problems in various ways. The
application of graph theory is a broad and mostly
represented in the programming, but can be applied in
everyday life, for example, when creating schedules, while
driving a car, walking, etc.

2. Working methods Chart No.1 - Presentation of survey results

It's composed out of the following paragraphs:  The optimal solution of the research was found by
23% of students.
- analysis of data collected from the literature
 The solution which path was up to 10% longer than
- analysis of previous research in this area
the optimal, was found by 29% of students.
- use of theoretical knowledge in solving problems
 The solution which path was more than 10% longer
- implementation of the survey than the optimal, was found by 48% of students.

4. Conclusion

With the analysis of the survey results, we see that a large
number of students found a solution that does not meet the
needs of cost and time saving. This means that introducing
and applying the theory of graphs significantly relieves the
everyday problems, and thereby the save of time and
money would be much higher.
Picture No.1 - Creating a survey

5. Literature
3. The results of research
[1.] www. wikipedia.org/sr-ec/Теорија_графова
The research results represent an analysis of a survey that [2.] Vladimir Baltić, "Graph theory for students of
was conducted. The task was: We observe the plan of University of Organizational Science who listen to
excursion: departure from Belgrade, entry into Italy late in Discret mathematical structures", Belgrade, 2008
the evening, going to hotels and accommodation during the
night. It is necessary to visit 6 places / cities (San Marino, [3.] www.viser.edu.rs/download.php?id=7040
Florence, Siena, Venice, Verona and Pisa), except that [4.] http://www.selimbegovic.com/Dokumenti/Metricki
accommodation in hotels is possible in just 3 places %20problemi%20u%20teoriji%20grafova.pdf
(Rimini, Montekatini Terme and Lido di Jesolo).It is [5.] Dragan Stevanović, Marko Milošević, Vladimir
possible to visit only one city per day, and at night, it is Baltić, " Discreet Mathematics, Basics of
obligated to return to hotels. The first picture shows cities Combinatorics and Graph theory, Workbook",
and their marks on the map, and the second picture shows Belgrade, 2004