Graph Edge
المؤلف:
Harary, F.
المصدر:
Graph Theory. Reading, MA: Addison-Wesley, 1994.
الجزء والصفحة:
...
18-3-2022
2526
Graph Edge
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 
nodes.
| graph |
OEIS |
 , 2, ... |
| graph |
A086314 |
0, 1, 6, 33, 170, 1170, 10962, 172844, 4944024, ... |
| labeled graph |
A095351 |
0, 1, 12, 192, 5120, 245760, 22020096, ... |
| labeled tree |
A053506 |
0, 1, 6, 48, 500, 6480, ... |
| planted tree |
A055544 |
0, 1, 2, 6, 16, 45, 120, 336, 920, 2574, 7190, 20262, ... |
| rooted tree |
A095350 |
0, 1, 4, 12, 36, 100, 288, 805, 2288, 6471, 18420, 52426, ... |
| tree |
A095349 |
0, 1, 2, 6, 12, 30, 66, 161, 376, 954, 2350, 6061, 15612, 41067, ... |
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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