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Graph Edge


GraphNodesEdges

For an undirected graph, an unordered pair of nodes that specify a line joining these two nodes are said to form an edge. For a directed graph, the edge is an ordered pair of nodes. The terms "arc," "branch," "line," "link," and "1-simplex" are sometimes used instead of edge (e.g., Skiena 1990, p. 80; Harary 1994). Harary (1994) calls an edge of a graph a "line."

The following table lists the total number of edges in all graphs of given classes on n nodes.

graphOEISn=1, 2, ...
graphA0863140, 1, 6, 33, 170, 1170, 10962, 172844, 4944024, ...
labeled graphA0953510, 1, 12, 192, 5120, 245760, 22020096, ...
labeled treeA0535060, 1, 6, 48, 500, 6480, ...
planted treeA0555440, 1, 2, 6, 16, 45, 120, 336, 920, 2574, 7190, 20262, ...
rooted treeA0953500, 1, 4, 12, 36, 100, 288, 805, 2288, 6471, 18420, 52426, ...
treeA0953490, 1, 2, 6, 12, 30, 66, 161, 376, 954, 2350, 6061, 15612, 41067, ...

See also

Edge Count, Graph Vertex, Hyperedge, Null Graph, Tait Coloring, Tait Cycle

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References

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.Sloane, N. J. A. Sequences A053506, A055544, A086314, A095349, A095350, and A095351 in "The On-Line Encyclopedia of Integer Sequences."

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Graph Edge

Cite this as:

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

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