05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15)
 05C05 Trees
 05C07 Vertex degrees [See also 05E30]
 05C10 Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]

05C12 Distance in graphs
(1)
 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
 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
(1)
 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]
 05C99 None of the above, but in this section