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A167227 Number of 2-self-hedrites with n vertices. 2
1, 1, 2, 2, 3, 3, 3, 3, 5, 4, 4, 6, 5, 5, 8, 5, 6, 8, 6, 8, 10, 7, 7, 10, 10, 8, 12, 10, 9, 14, 9, 9, 14, 10, 14, 16, 11, 11, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

From Table 2, p.11, of Sikiric. Number of 2-self-hedrites with 4 <= n <= 40 and 2 <= i <= 4. An i-hedrite is a 4-regular plane graph with faces of size 2, 3 and 4. We do a short survey of their known properties and explain some new algorithms that allow their efficient enumeration. Using this we give the symmetry groups of all i-hedrites and the minimal representative for each. We also review the link of 4-hedrites with knot theory and the classification of 4-hedrites with simple central circuits. An i-self-hedrite is a self-dual plane graph with faces and vertices of size/degree 2, 3 and 4. We give a new efficient algorithm for enumerating them based on i-hedrites. We give a classification of their possible symmetry groups and a classification of 4-self-hedrites of symmetry T, Td in terms of the Goldberg-Coxeter construction. Then we give a method for enumerating 4-self-hedrites with simple zigzags.

LINKS

Table of n, a(n) for n=2..40.

Mathieu Dutour Sikiric, Michel Deza, 4-regular and self-dual analogs of fullerenes, Oct 28, 2009.

CROSSREFS

Cf. A167156-A167160, A167228, A167229.

Sequence in context: A284523 A034584 A035430 * A048280 A024695 A259195

Adjacent sequences:  A167224 A167225 A167226 * A167228 A167229 A167230

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Oct 30 2009

STATUS

approved

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Last modified September 28 16:40 EDT 2020. Contains 337393 sequences. (Running on oeis4.)