# 1. Objective / Мета роботи

**Understand the basic notions of graph theory and implement the core operations
on graphs — degrees, matrix representations, paths, and graph comparison.**

By the end of the work the student should be able to:

- represent an undirected **graph** by its vertices and edges, and compute the
  **degree** of each vertex;
- verify the **handshaking theorem** — the sum of all degrees equals twice the
  number of edges;
- build the **adjacency matrix** and the **incidence matrix** of a graph;
- **find a path** between two vertices, and discover a **circuit** (closed trail);
- distinguish **walks, trails, and paths**, and enumerate them between two
  vertices;
- test whether one graph is a **subgraph** of another, and whether two graphs are
  **isomorphic**;
- reason about the **time complexity** of these operations.

The work establishes the vocabulary and representations of graph theory that the
rest of the course — traversal, shortest paths, trees, and colourings — builds on.