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A319490 Number of non-isomorphic connected graphs on n vertices with representation number 3. 1
0, 0, 0, 0, 0, 1, 39, 1852, 88838 (list; graph; refs; listen; history; text; internal format)



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.


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.


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.


Cf. A319489 (graphs with representation number 2).

Sequence in context: A269028 A158768 A139191 * A327589 A176073 A145619

Adjacent sequences:  A319487 A319488 A319489 * A319491 A319492 A319493




Sergey Kitaev, Sep 20 2018



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Last modified December 6 13:45 EST 2021. Contains 349563 sequences. (Running on oeis4.)