Graph operations

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Graph operations produce new graphs from initial ones. They may be separated into the following major categories.

Unary operations[edit]

Unary operations create a new graph from one initial one.

Elementary operations[edit]

Elementary operations or editing operations create a new graph from one initial one by a simple local change, such as addition or deletion of a vertex or of an edge, merging and splitting of vertices, edge contraction, etc. The graph edit distance between a pair of graphs is the minimum number of elementary operations required to transform one graph into the other.

Advanced operations[edit]

Advanced operations create a new graph from one initial one by a complex changes, such as:

Binary operations[edit]

Binary operations create a new graph from two initial ones G1 = (V1, E1) and G2 = (V2, E2), such as:

  • graph union: G1G2 = (V1V2, E1E2). When V1 and V2 are disjoint, the graph union is referred to as the disjoint graph union, and denoted G1 + G2;[1]
  • graph intersection: G1G2 = (V1V2, E1E2);[1]
  • graph join: graph with all the edges that connect the vertices of the first graph with the vertices of the second graph. It is a commutative operation (for unlabelled graphs);[2]
  • graph products based on the cartesian product of the vertex sets:
  • graph product based on other products:
  • series-parallel graph composition:
    • parallel graph composition: it is a commutative operation (for unlabelled graphs),
    • series graph composition: it is a non-commutative operation,
    • source graph composition: it is a commutative operation (for unlabelled graphs);
  • Hajós construction.

Notes[edit]

  1. ^ a b Bondy, J. A.; Murty, U. S. R. (2008). Graph Theory. Graduate Texts in Mathematics. Springer. p. 29. ISBN 978-1-84628-969-9. 
  2. ^ a b c Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.
  3. ^ Reingold, O.; Vadhan, S.; Wigderson, A. (2002). "Entropy waves, the zig-zag graph product, and new constant-degree expanders". Annals of Mathematics 155 (1): 157–187. doi:10.2307/3062153. JSTOR 3062153. MR 1888797. 
  4. ^ Robert Frucht and Frank Harary. "On the coronas of two graphs", Aequationes Math., 4:322–324, 1970.