A366315 Number of Harris graphs with n vertices. Harris graphs are 1-tough, Eulerian graphs that are non-Hamiltonian.

0, 0, 0, 0, 0, 0, 1, 3, 26, 340, 7297, 233608

Offset

1,8

Comments

There are no Harris graphs with 6 or fewer vertices.

Links

Table of n, a(n) for n=1..12.

Francesca Gandini, Shubhra Mishra, and Douglas Shaw, Families of Harris Graphs, arXiv:2312.10936 [math.CO], 2023.

Shubhra Mishra, Illustration for a(7) = 1: the unique minimal Harris graph of order 7

Shubhra Mishra, Illustration for a(8) = 3: the three order 8 Harris graphs

Douglas J. Shaw, Harris Graphs--A Graph Theory Activity for Students and Their Instructors, The College Mathematics Journal, 49 (2018), 5, 323-326.

Example

a(7)=1 because the only Harris graph of 7 vertices (0..6) has edges {(0,1), (0,2), (0,3), (0,4), (1,2), (1,3), (1,5), (2,3), (2,6), (3,4), (3,5), (3,6)}. - Sean A. Irvine, Oct 18 2023

Crossrefs

Cf. A007031.

Sequence in context: A227020 A119293 A339298 * A328269 A136046 A206404

Adjacent sequences: A366312 A366313 A366314 * A366316 A366317 A366318

Keyword

nonn,more,hard

Author

Shubhra Mishra, Oct 06 2023

Extensions

a(11)-a(12) from Sean A. Irvine, Oct 18 2023

Status

approved