A078639 Number of nonisomorphic graphic matroids of connected graphs on n vertices (equivalently, of rank n-1).

1, 1, 2, 5, 16, 73, 533, 7303

Offset

1,3

Links

Table of n, a(n) for n=1..8.

Example

Out of 6 simple connected graphs on n = 4 vertices, two are trees (the path and the claw), while all others have nonisomorphic matroids; a graphic matroid of a tree is free and therefore is unique for a given number of vertices, so the matroids of these two trees are isomorphic, and a(4) = 6-1 = 5.

Prog

(SageMath)
def a(n):
    matroids = []
    for G in graphs.nauty_geng(f"{n} -c"):
        M = Matroid(G)
        for N in matroids:
            if M.is_isomorphic(N):
                break
        else:
            matroids.append(M)
    return len(matroids) # Andrei Zabolotskii, Feb 18 2026

Crossrefs

Sequence in context: A381515 A395521 A245881 * A002632 A020127 A179500

Adjacent sequences: A078636 A078637 A078638 * A078640 A078641 A078642

Keyword

nonn,more

Author

Gordon Royle, Oct 06 2008

Extensions

Name clarified and a(1) inserted by Andrei Zabolotskii, Feb 18 2026

Status

approved