Graph Center

The center of a graph  is the set of vertices of graph eccentricity equal to the graph radius (i.e., the set of central points). In the above illustration, center nodes are shown in red.

The center of a graph may be computed in the Wolfram Language with the command GraphCenter[g].

The following table gives the number of -node simple unlabeled graphs having  center nodes.

	OEIS	, 2, ...
1	A052437	1, 0, 1, 2, 8, 29, 180, ...
2	A052438	0, 2, 0, 2, 4, 19, 84, ...
3	A052439	0, 0, 3, 0, 4, 18, 119, ...
4	A052340	0, 0, 0, 7, 0, 18, 118, ...
5	A052341	0, 0, 0, 0, 18, 0, 129, ...
6		0, 0, 0, 0, 0, 72, 0, ...
7		0, 0, 0, 0, 0, 0, 414, ...

REFERENCES

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 35, 1994.

Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 107, 1990.

Sloane, N. J. A. Sequences A052437, A052438, A052439, A052340, and A052341 in "The On-Line Encyclopedia of Integer Sequences."