2019
DOI: 10.1016/j.disc.2019.04.009
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On factor-invariant graphs

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Cited by 4 publications
(4 citation statements)
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“…the case for the generalized Petersen graphs, solutions to (5) where = kj are exactly the solution to (3). We see that if k is even, then j n , jk n is either 1 4 , k 4 or 3 4 , 3k 4 , neither of which can be a subset of 1 4 , 3 4 since k is even. Thus, in this case, 1 is a simple eigenvalue.…”
Section: Generalized Petersen Graphsmentioning
confidence: 87%
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“…the case for the generalized Petersen graphs, solutions to (5) where = kj are exactly the solution to (3). We see that if k is even, then j n , jk n is either 1 4 , k 4 or 3 4 , 3k 4 , neither of which can be a subset of 1 4 , 3 4 since k is even. Thus, in this case, 1 is a simple eigenvalue.…”
Section: Generalized Petersen Graphsmentioning
confidence: 87%
“…Let α (0 ≤ α ≤ k) be the number of neighbours y of x such that v(y) = −1. Then (1) implies that λ = k − 2α.…”
Section: Partitions and Eigenvectorsmentioning
confidence: 99%
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“…∎ Lemma 4.1 motivates the question to classify cubic vertex-transitive graphs that admit a decomposition into a "bipartite" 2-factor and a perfect matching, where both factors are invariant under the full automorphism group. Inspired by this problem, Alspach, Khodadadpour, and Kreher [1] classified all cubic vertex-transitive graphs containing a Hamilton cycle that is invariant under the action of the automorphism group. In Section 6, we classify the cases when G[V + ] is a single cycle and when the cycles in G[V + ] are triangles, respectively.…”
Section: Combinatorial Structurementioning
confidence: 99%