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Graph Join


GraphJoin

The join G=G_1+G_2 of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph union G_1 union G_2 together with all the edges joining V_1 and V_2 (Harary 1994, p. 21). Graph joins are implemented in the Wolfram Language as GraphJoin[G1, G2].

A complete k-partite graph K_(i,j,...) is the graph join of empty graphs on i, j, ... nodes. A wheel graph is the join of a cycle graph and the singleton graph. Finally, a star graph is the join of an empty graph and the singleton graph (Skiena 1990, p. 132).

The following table gives examples of some graph joins. Here K^__n denotes an empty graph (i.e., the graph complement of the complete graph K_n), C_n a cycle graph, and K_1 the singleton graph.


See also

Cone Graph, Dipyramidal Graph, Fan Graph, Graph Cartesian Product, Graph Sum, Graph Union, Star Graph, Wheel Graph, Windmill Graph

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References

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.Skiena, S. "Joins of Graphs." §4.1.3 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 131-132, 1990.

Referenced on Wolfram|Alpha

Graph Join

Cite this as:

Weisstein, Eric W. "Graph Join." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphJoin.html

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