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The packing number of the double vertex graph of the path graph

LUIS MANUEL RIVERA MARTINEZ (2018)

Neil Sloane showed that the problem of determining the maximum size of a binary code of

constant weight 2 that can correct a single adjacent transposition is equivalent to finding

the packing number of a certain graph. In this paper we solve this open problem by finding

the packing number of the double vertex graph of the path graph. This double vertex graph

is isomorphic to Sloane’s graph. Our solution implies a conjecture of Rob Pratt about the

ordinary generating function of sequence A085680.

Producción Científica de la Universidad Autónoma de Zacatecas UAZ

Article

CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Double vertex graph Packing number Error correcting codes Binary codes