cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A381765 Number of connected simple graphs on n unlabeled vertices whose degree sequence is consecutive.

Original entry on oeis.org

1, 1, 1, 2, 5, 16, 75, 544, 6920, 159228, 6961507, 577826609, 90529308665
Offset: 0

Views

Author

John P. McSorley, Mar 25 2025

Keywords

Comments

A connected graph has a consecutive degree sequence if its distinct degrees are consecutive integers. This includes all connected regular graphs.

Examples

			For n = 4 there are 6 non-isomorphic connected graphs G on 4 vertices. An example with consecutive degree sequence is P_4, the path on 4 vertices, with degree sequence 1122; and an example with non-consecutive degree sequence is the star K_{1,3} with degree sequence 1113. All other connected G have consecutive degree sequence. Thus a(4) = 5.

References

  • R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford University Press (1999).

Crossrefs

Cf. A381586, A001349, A005177.

Extensions

a(7)-a(10) from Andrew Howroyd, Mar 26 2025
a(11)-a(12) from Sean A. Irvine, Apr 01 2025

A382021 Number of distinct degree sequences among all simple graphs with n vertices whose degrees are consecutive integers.

Original entry on oeis.org

1, 1, 2, 4, 9, 21, 50, 118, 272, 614, 1368, 3014
Offset: 0

Views

Author

John P. McSorley, Mar 12 2025

Keywords

Comments

A sequence of integers is consecutive if its distinct entries are consecutive integers, and a graphic sequence is a sequence of integers that can be the degree sequence of some graph. Thus a(n) is the number of consecutive graphic sequences of length n.

Examples

			For n = 5 there are 34 non-isomorphic graphs G on 5 vertices, and 24 of these have a consecutive degree sequence. However consecutive degree sequences 11222, 12223, and 22233 each correspond to 2 non-isomorphic graphs. Thus there are 21 distinct consecutive graphic sequences of length 5, and so a(5)=21.

References

  • R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford University Press (1999).

Crossrefs

Cf. A381586, A000088, A004251, A005176.

Extensions

a(11) from Sean A. Irvine, Mar 18 2025
Showing 1-2 of 2 results.

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