Graph Vertex

"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 ...

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."