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 . \[ \begin{array}{l} G=(V, E), V=\{1,2,3,4,5\}, \quad E=\{(1,2),(1,3), \\ (1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)\} . \end{array} \]