\contentsline {part}{I\hspace {1em}Fundamentals}{1}{part.1}%
\contentsline {chapter}{\numberline {1}Graphs}{3}{chapter.1}%
\contentsline {section}{\numberline {1.1}Undirected graphs}{4}{section.1.1}%
\contentsline {section}{\numberline {1.2}Loops}{5}{section.1.2}%
\contentsline {section}{\numberline {1.3}Directed graphs}{5}{section.1.3}%
\contentsline {section}{\numberline {1.4}Weighted graphs}{6}{section.1.4}%
\contentsline {section}{\numberline {1.5}Graph isomorphsim}{6}{section.1.5}%
\contentsline {chapter}{\numberline {2}Features of graphs}{7}{chapter.2}%
\contentsline {section}{\numberline {2.1}Degree}{7}{section.2.1}%
\contentsline {section}{\numberline {2.2}Graph matrixes}{7}{section.2.2}%
\contentsline {section}{\numberline {2.3}Paths}{8}{section.2.3}%
\contentsline {subsection}{\numberline {2.3.1}Connected graphs}{8}{subsection.2.3.1}%
\contentsline {subsection}{\numberline {2.3.2}Kőnig's lemma}{8}{subsection.2.3.2}%
\contentsline {section}{\numberline {2.4}Cycles}{9}{section.2.4}%
\contentsline {section}{\numberline {2.5}Trees}{9}{section.2.5}%
\contentsline {subsection}{\numberline {2.5.1}Propositions on trees}{9}{subsection.2.5.1}%
\contentsline {subsection}{\numberline {2.5.2}Cayley's formula}{9}{subsection.2.5.2}%
\contentsline {section}{\numberline {2.6}Directed acyclic graph}{9}{section.2.6}%
\contentsline {chapter}{\numberline {3}Euler's formula}{11}{chapter.3}%
\contentsline {section}{\numberline {3.1}3 Utilities problem}{11}{section.3.1}%
\contentsline {section}{\numberline {3.2}Euler's formula}{11}{section.3.2}%
\contentsline {section}{\numberline {3.3}Solving the 3 utilities problem}{12}{section.3.3}%
\contentsline {part}{II\hspace {1em}Advanced}{13}{part.2}%
\contentsline {chapter}{\numberline {4}Topological graph theory}{15}{chapter.4}%
\contentsline {chapter}{\numberline {5}Algebraic graph theory}{17}{chapter.5}%