Families of Integral Cographs within a Triangular Array
| Autor: | Rigoberto Flórez, Antara Mukherjee, Hsin-Yun Ching |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
Fibonacci number adjacency matrix integral graph secondary 11b39 fibonacci number determinant hosoya triangle Combinatorics QA1-939 eigenvalue Integral graph Cograph Geometry and Topology Adjacency matrix cograph primary 68r11 Triangular array Mathematics Eigenvalues and eigenvectors |
| Zdroj: | Special Matrices, Vol 8, Iss 1, Pp 257-273 (2020) |
| ISSN: | 2300-7451 |
| DOI: | 10.1515/spma-2020-0116 |
| Popis: | The determinant Hosoya triangle, is a triangular array where the entries are the determinants of two-by-two Fibonacci matrices. The determinant Hosoya triangle mod 2 gives rise to three infinite families of graphs, that are formed by complete product (join) of (the union of) two complete graphs with an empty graph. We give a necessary and sufficient condition for a graph from these families to be integral.Some features of these graphs are: they are integral cographs, all graphs have at most five distinct eigenvalues, all graphs are either d-regular graphs with d =2, 4, 6, . . . or almost-regular graphs, and some of them are Laplacian integral. Finally we extend some of these results to the Hosoya triangle. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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