A complete characterization of bidegreed split graphs with four distinct signless Laplacian eigenvalues
| Autor: | Guanbang Song, Guifu Su, Huichao Shi |
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| Rok vydání: | 2021 |
| Předmět: |
Vertex (graph theory)
Numerical Analysis Algebra and Number Theory Mathematics::Spectral Theory Characterization (mathematics) Clique (graph theory) Combinatorics Set (abstract data type) Combinatorial design Independent set Discrete Mathematics and Combinatorics Geometry and Topology Split graph Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Linear Algebra and its Applications. 629:232-245 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2021.08.006 |
| Popis: | It is a well-known fact that a graph of diameter d has at least d + 1 eigenvalues (A.E. Brouwer, W.H. Haemers (2012) [2] ). A graph is d-extremal (resp. d S L -extremal) if it has diameter d and exactly d + 1 distinct eigenvalues (resp. signless Laplacian eigenvalues), and a graph is split if its vertex set can be partitioned into a clique and a stable set. Such graphs have diameter at most three. If all vertex degrees in a split graph are either d ˜ or d ˆ , then we say it is ( d ˜ , d ˆ ) -bidegreed. In this paper, we present a complete classification of the connected bidegreed 3 S L -extremal split graphs using the association of split graphs with combinatorial designs. |
| Databáze: | OpenAIRE |
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