
6.4.7 Graph theory
Problem:
1. Write a route, a chain, a simple chain, a cycle, a simple cycle, an adjacency matrix (neighborhood of vertices) and an incidence matrix (belonging to vertices and edges) for the given undirected graph. Convert the given undirected graph into a directed one and write for it a route, a path, a simple path, a contour, a simple contour, an adjacency matrix and an incidence matrix.
2. For the given graph, find the shortest distance for all vertices from vertex 2 .
\[
\begin{array}{l}
G=(V, E), V=\{1,2,3,4,5\}, \quad E=\{(1,2),(1,3), \\
(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)\} .
\end{array}
\]