Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949822 | Discrete Applied Mathematics | 2017 | 11 Pages |
Abstract
We study the Laplacian and the signless Laplacian energy of connected unicyclic graphs, obtaining a tight upper bound for this class of graphs. We also find the connected unicyclic graph on n vertices having largest (signless) Laplacian energy for 3â¤nâ¤13. For nâ¥11, we conjecture that the graph consisting of a triangle together with nâ3 balanced distributed pendent vertices is the candidate having the maximum (signless) Laplacian energy among connected unicyclic graphs on n vertices. We prove this conjecture for many classes of graphs, depending on Ï, the number of (signless) Laplacian eigenvalues bigger than or equal to 2.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Kinkar Ch. Das, Eliseu Fritscher, Lucélia Kowalski Pinheiro, Vilmar Trevisan,