|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||Abstract:||
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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