4-regular integral graphs avoiding ±3 in the spectrum

Stevanović, Dragan

doi:10.2298/petf0314099s

Cited by 17 publications

(12 citation statements)

References 6 publications

(6 reference statements)

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“…Similar to the result by Schwenk [20] used in [24] and [25], we have that if G is a QIG, then the bipartite double cover of G is a bipartite QIG. If G is a bipartite QIG then the bipartite double cover consists of two disjoint copies of G. For this reason, we have restricted our search to integral graphs that are bipartite up to this point.…”

Section: Integral Graphs As Quotientssupporting

confidence: 77%

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Quartic integral Cayley graphs

Minchenko

Wanless

2015

Ars Math. Contemp.

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We give exhaustive lists of connected 4-regular integral Cayley graphs and connected 4-regular integral arc-transitive graphs. An integral graph is a graph for which all eigenvalues are integers. A Cayley graph Cay(Γ, S) for a given group Γ and connection set S ⊂ Γ is the graph with vertex set Γ and with a connected to b if and only if ba −1 ∈ S. Up to isomorphism, we find that there are 32 connected quartic integral Cayley graphs, 17 of which are bipartite. Many of these can be realized in a number of different ways by using non-isomorphic choices for Γ and/or different choices for S. A graph is arc-transitive if its automorphism group acts transitively on the ordered pairs of adjacent vertices. Up to isomorphism, there are 27 quartic integral graphs that are arc-transitive. Of these 27 graphs, 16 are bipartite and 16 are Cayley graphs. By taking quotients of our Cayley or arc-transitive graphs we also find a number of other quartic integral graphs. Overall, we find 9 new spectra that can be realised by bipartite quartic integral graphs.

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Section: Integral Graphs As Quotientssupporting

confidence: 77%

“…Useful tools include an identity by Hoffman [11] and equations relating the spectral moments to the closed walks of length 6. All QIGs that avoid eigenvalues of ±3 and realize a possible spectrum are found in [24]. Stevanović [23] eliminates spectra using equations arising from graph angles.…”

Section: Introductionmentioning

confidence: 99%

Quartic integral Cayley graphs

Minchenko

Wanless

2015

Ars Math. Contemp.

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“…Radosavljević and Simić in [19] determined all thirteen nonregular nonbipartite connected integral graphs with maximum degree four. Stevanović [22] determined all connected 4-regular integral graphs avoiding ±3 in the spectrum. A survey of results on integral graphs may be found in [6].…”

Section: Introduction and Resultsmentioning

confidence: 99%

Integral Quartic Cayley Graphs on Abelian Groups

Abdollahi

Vatandoost

2011

Electron. J. Combin.

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“…In 1970s, Cvetković [2] and Schwenk [12] classified the connected integral graphs of maximum degree at most 3. Stevanović [13] determined the 4-regular integral graphs avoiding ±3 in the spectrum and gave the possible spectrum of 4-regular bipartite graphs. In 2008, Kirkland [10] proved that there are 21 connected Laplacian integral graphs of maximum degree 3 on at least 6 vertices.…”

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confidence: 99%