TOPICS
Search

Graph Union


GraphUnion

The union G=G_1 union 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 with V=V_1 union V_2 and X=X_1 union X_2 (Harary 1994, p. 21; Gross and Yellen 2006, p. 85).

When the vertices and edges of G_1 and G_2 are considered distinct regardless of their labels, the operation is sometimes known as the graph disjoint union in order to distinguish it from the graph union operation that merges vertices and edges with shared labels when taking the unions of edges and vertices in G_1 and G_2.

The Wolfram Language function GraphUnion[g1, g2] takes the graph union by merging labeled vertices and edges, while GraphDisjointUnion[g1, g2, ...] treats vertices and edges in the components as distinct regardless of their labels.

The graph disjoint union of n copies of a graph G is commonly denoted nG (Harary 1990, p. 21).


See also

Graph Intersection, Graph Join, Graph Sum

Explore with Wolfram|Alpha

References

Gross, J. T. and Yellen, J. Graph Theory and Its Applications, 2nd ed. Boca Raton, FL: CRC Press, 2006.Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 21, 1994.Skiena, S. "Unions and Intersections." §4.1.1 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 129-131, 1990.

Referenced on Wolfram|Alpha

Graph Union

Cite this as:

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

Subject classifications