Article ID Journal Published Year Pages File Type
4949822 Discrete Applied Mathematics 2017 11 Pages PDF
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 3≤n≤13. For n≥11, we conjecture that the graph consisting of a triangle together with n−3 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 σ, the number of (signless) Laplacian eigenvalues bigger than or equal to 2.
Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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