On the Laplacian Coefficients and Laplacian‐Like Energy of Unicyclic Graphs with n Vertices and m Pendent Vertices

Xinying Pai and Sanyang Liu

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: Let Φ(G,λ)=det(λIn-L(G))=∑k=0n(-1) kck(G)λn-k be the characteristic polynomial of the Laplacian matrix of a graph G of order n. In this paper, we give four transforms on graphs that decrease all Laplacian coefficients ck(G) and investigate a conjecture A. Ilić and M. Ilić (2009) about the Laplacian coefficients of unicyclic graphs with n vertices and m pendent vertices. Finally, we determine the graph with the smallest Laplacian‐like energy among all the unicyclic graphs with n vertices and m pendent vertices.

Date: 2012
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https://doi.org/10.1155/2012/404067

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:404067

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