A319490 - OEIS

A319490

Number of non-isomorphic connected graphs on n vertices with representation number 3.

0, 0, 0, 0, 0, 1, 39, 1852, 88838

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,7

COMMENTS

These are graphs that can be represented by words having three copies of each letter, but cannot be represented by words having two copies of each letter. In a word representing a graph G, letters x and y alternate if any only if there is an edge between x and y in G.

LINKS

Table of n, a(n) for n=1..9.

Ozgur Akgun, Ian P. Gent, Sergey Kitaev, Hans Zantema, Solving computational problems in the theory of word-representable graphs, arXiv:1808.01215 [math.CO], 2018.

Sergey Kitaev, A comprehensive introduction to the theory of word-representable graphs, arXiv:1705.05924 [math.CO], 2017.

EXAMPLE

The triangular prism is the only graph on 6 vertices that can be represented using three copies of each letter, but cannot be represented using 2 copies of each letter.

CROSSREFS

Cf. A319489 (graphs with representation number 2).

Sequence in context: A269028 A158768 A139191 * A327589 A176073 A145619

Adjacent sequences: A319487 A319488 A319489 * A319491 A319492 A319493

KEYWORD

nonn,more

AUTHOR

Sergey Kitaev, Sep 20 2018

STATUS

approved