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Jacobsthal Numbers in Generalized Petersen Graphs
Author(s) -
Bruhn Henning,
Gellert Laura,
Günther Jacob
Publication year - 2017
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22017
Subject(s) - mathematics , combinatorics , petersen graph , conjecture , graph , discrete mathematics , list coloring , line graph , voltage graph , graph power
We prove that the number of 1‐factorizations of a generalized Petersen graph of the type G P ( 3 k , k ) is equal to the k th Jacobsthal number J ( k ) when k is odd, and equal to 4 J ( k ) when k is even. Moreover, we verify the list coloring conjecture for G P ( 3 k , k ) .