Maximality of the signless Laplacian energy
| Autor: | Vilmar Trevisan, Lucélia Kowalski Pinheiro |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
0211 other engineering and technologies 021107 urban & regional planning 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences 1-planar graph Theoretical Computer Science Combinatorics Independent set Discrete Mathematics and Combinatorics Cograph Graph homomorphism Split graph Graph coloring Graph toughness 0101 mathematics Pancyclic graph Mathematics |
| Zdroj: | Discrete Mathematics. 341:33-41 |
| ISSN: | 0012-365X |
| Popis: | We study the problem of determining the graph with n vertices having largest signless Laplacian energy. We conjecture it is the complete split graph whose independent set has (roughly) 2 n ∕ 3 vertices. We show that the conjecture is true for several classes of graphs. In particular, the conjecture holds for the set of all complete split graphs of order n , for trees, for unicyclic and bicyclic graphs. We also give conditions on the number of edges, number of cycles and number of small eigenvalues so the graph satisfies the conjecture. |
| Databáze: | OpenAIRE |
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