Graph Vertex (original) (raw)
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"Vertex" is a synonym for a node of a graph, i.e., one of the points on which the graph is defined and which may be connected by graph edges. The terms "point," "junction," and 0-simplex are also used (Harary 1994; Skiena 1990, p. 80).
The following tables gives the total numbers of graph vertices for various classes of graphs on 
, 2, ... nodes.
| graph type | OEIS | total node count for  , 2, ... nodes |
|---|---|---|
| graph | A055542 | 1, 4, 12, 44, 170, 936, 7308, 98768, 2472012, ... |
| labeled graph | A095340 | 1, 4, 24, 256, 5120, 196608, ... |
| labeled tree | A000169 | 1, 2, 9, 64, 625, 7776, 117649, ... |
| planted tree | A095341 | 0, 2, 3, 8, 20, 54, 140, 384, 1035, 2860, ... |
| rooted tree | A055545 | 1, 2, 6, 16, 45, 120, 336, 920, 2574, ... |
| tree | A055544 | 1, 2, 3, 8, 15, 36, 77, 184 ... |
See also
Graph, Graph Edge, Null Graph, Polygon Vertex, Tait Coloring, Tait Cycle, Tait's Hamiltonian Graph Conjecture
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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 A000169/M1946,A055542, A055544,A055545, and A095340 in "The On-Line Encyclopedia of Integer Sequences."
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Cite this as:
Weisstein, Eric W. "Graph Vertex." FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphVertex.html