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A Complete Characterization of Bidegreed Split Graphs with Four Distinct α -Eigenvalues.
- Source :
-
Symmetry (20738994) . May2022, Vol. 14 Issue 5, p899-899. 12p. - Publication Year :
- 2022
-
Abstract
- It is a well-known fact that a graph of diameter d has at least d + 1 eigenvalues. A graph is d-extremal (resp. d α -extremal) if it has diameter d and exactly d + 1 distinct eigenvalues (resp. α -eigenvalues), and a graph is split if its vertex set can be partitioned into a clique and a stable set. Such graphs have a diameter of at most three. If all vertex degrees in a split graph are either d ˜ or d ^ , then we say it is (d ˜ , d ^) -bidegreed. In this paper, we present a complete classification of the connected bidegreed 3 α -extremal split graphs using the association of split graphs with combinatorial designs. This result is a natural generalization of Theorem 4.6 proved by Goldberg et al. and Proposition 3.8 proved by Song et al., respectively. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EIGENVALUES
*CHARTS, diagrams, etc.
*GENERALIZATION
*DIAMETER
*SONGS
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 14
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 157238731
- Full Text :
- https://doi.org/10.3390/sym14050899