## 05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15)

- 05C05 Trees (2)
- 05C07 Vertex degrees [See also 05E30]
- 05C10 Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]
- 05C12 Distance in graphs
- 05C15 Coloring of graphs and hypergraphs
- 05C17 Perfect graphs
- 05C20 Directed graphs (digraphs), tournaments
- 05C21 Flows in graphs
- 05C22 Signed and weighted graphs
- 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]
- 05C30 Enumeration in graph theory (1)
- 05C31 Graph polynomials
- 05C35 Extremal problems [See also 90C35]
- 05C38 Paths and cycles [See also 90B10]
- 05C40 Connectivity
- 05C42 Density (toughness, etc.)
- 05C45 Eulerian and Hamiltonian graphs
- 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
- 05C51 Graph designs and isomomorphic decomposition [See also 05B30]
- 05C55 Generalized Ramsey theory [See also 05D10]
- 05C57 Games on graphs [See also 91A43, 91A46]
- 05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
- 05C62 Graph representations (geometric and intersection representations, etc.) For graph drawing, see also 68R10
- 05C63 Infinite graphs
- 05C65 Hypergraphs
- 05C69 Dominating sets, independent sets, cliques
- 05C70 Factorization, matching, partitioning, covering and packing
- 05C72 Fractional graph theory, fuzzy graph theory
- 05C75 Structural characterization of families of graphs
- 05C76 Graph operations (line graphs, products, etc.)
- 05C78 Graph labelling (graceful graphs, bandwidth, etc.)
- 05C80 Random graphs [See also 60B20]
- 05C81 Random walks on graphs
- 05C82 Small world graphs, complex networks [See also 90Bxx, 91D30]
- 05C83 Graph minors
- 05C85 Graph algorithms [See also 68R10, 68W05]
- 05C90 Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15] (1)
- 05C99 None of the above, but in this section