A319489 - OEIS

A319489

Number of non-isomorphic connected graphs on n vertices with representation number 2.

0, 0, 1, 5, 20, 109, 788, 8335, 117282, 2026330, 40302424, 892278075

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

OFFSET

1,4

COMMENTS

These are graphs that can be represented by words having two copies of each letter, but cannot be represented by words having one copy of each letter. In a word representing a graph G, letters x and y alternate if and only if there is an edge between x and y in G. Such graphs, along with complete graphs, are precisely the class of circle graphs.

LINKS

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

Ozgur Akgun, Ian P. Gent, Sergey Kitaev, and 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

For n=3 there is one connected graph with vertex set, say, {1,2}, which is represented by 1212.

CROSSREFS

Equals A156808 minus 1; graphs with representation number 3 are in A319490.

Sequence in context: A277032 A300490 A020039 * A207972 A117736 A258665

Adjacent sequences: A319486 A319487 A319488 * A319490 A319491 A319492

KEYWORD

nonn,more

AUTHOR

Sergey Kitaev, Sep 20 2018

STATUS

approved