Extremal Laplacian energy of directed trees, unicyclic digraphs and bicyclic digraphs

Xiuwen Yang and Ligong Wang

Applied Mathematics and Computation, 2020, vol. 366, issue C

Abstract: Let A(G) and D+(G) be the adjacency matrix of a digraph G with n vertices and the diagonal matrix of vertex outdegrees of G, respectively. Then the Laplacian matrix of the digraph G is L(G)=D+(G)−A(G). The Laplacian energy of a digraph G is defined as LE(G)=∑i=1nλi2 by using second spectral moment, where λ1,λ2,…,λn are all the eigenvalues of L(G) of G. In this paper, by using arc shifting operation and out-star shifting operation, we determine the directed trees, unicyclic digraphs and bicyclic digraphs which attain maximal and minimal Laplacian energy among all digraphs with n vertices, respectively.

Keywords: Laplacian energy; Directed trees; Unicyclic digraphs; Bicyclic digraphs (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307295

DOI: 10.1016/j.amc.2019.124737

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