On split graphs with four distinct eigenvalues

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Date
2020
Authors
Goldberg, F.
Kirkland, S.
Varghese, A.
Vijayakumar, A.
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Journal ISSN
Volume Title
Publisher
Discrete Applied Mathematics
Abstract
It 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.
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Keywords
Adjacency matrix, Split graph, Bidegreed graph, Combinatorial design
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