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

Xiuwen Yang, Ligong Wang

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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=1 nλi 2 by using second spectral moment, where λ12,…,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.

Original languageEnglish
Article number124737
JournalApplied Mathematics and Computation
Volume366
DOIs
StatePublished - 1 Feb 2020

Keywords

  • Bicyclic digraphs
  • Directed trees
  • Laplacian energy
  • Unicyclic digraphs

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