On split graphs with four distinct eigenvalues

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dc.contributor.authorGoldberg, F.
dc.contributor.authorKirkland, S.
dc.contributor.authorVarghese, A.
dc.contributor.authorVijayakumar, A.
dc.date.accessioned2020-07-31T15:58:06Z
dc.date.available2020-07-31T15:58:06Z
dc.date.issued2020
dc.date.submitted2020-07-31T01:13:12Zen_US
dc.description.abstractIt is a well-known fact that a graph of diameter d has at least d + 1 eigenvalues. A graph is d-extremal, if it has diameter d and exactly d+1 eigenvalues. A graph is split if its vertex set can be partitioned into a clique and a stable set. Such graphs have diameter at most 3. We obtain a complete classification of the connected bidegreed 3-extremal split graphs using the association of split graphs with combinatorial designs. We also construct certain families of non-bidegreed 3-extremal split graphs.en_US
dc.description.sponsorshipNSERC grant number RGPIN/6123-2014. Science Foundation Ireland grant number SFI/07/SK/I1216b.en_US
dc.identifier.urihttp://hdl.handle.net/1993/34814
dc.language.isoengen_US
dc.publisherDiscrete Applied Mathematicsen_US
dc.rightsrestricted accessen_US
dc.statusyes
dc.subjectAdjacency matrixen_US
dc.subjectSplit graphen_US
dc.subjectBidegreed graphen_US
dc.subjectCombinatorial designen_US
dc.titleOn split graphs with four distinct eigenvaluesen_US
dc.typeArticleen_US
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