Authors: Stevanović, Dragan 
Ilić, Aleksandar
Title: On the Laplacian coefficients of unicyclic graphs
Journal: Linear Algebra and Its Applications
Volume: 430
Issue: 8-9
First page: 2290
Last page: 2300
Issue Date: 15-Apr-2009
Rank: M22
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.12.006
Let G be a graph of order n and let P (G, λ) = ∑k = 0n (- 1)k ck λn - k be the characteristic polynomial of its Laplacian matrix. Generalizing an approach of Mohar on graph transformations, we show that among all connected unicyclic graphs of order n, the kth coefficient ck is largest when the graph is a cycle Cn and smallest when the graph is the a Sn with an additional edge between two of its pendent vertices. A relation to the recently established Laplacian-like energy of a graph is discussed.
Keywords: Laplacian coefficients | Laplacian matrix | Laplacian-like energy | Unicyclic graph
Publisher: Elsevier
Project: Serbian Ministry of Science and Technological Development, Grants 144007 and 144015G
Slovenian Agency for Research, program P1-0285

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