Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2016, Vol. 33 ›› Issue (5): 534-540.doi: 10.3969/j.issn.1005-3085.2016.05.008

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General Coulson-type Integral Formula for the Energy of Digraphs

GAO Nan1,  LV Wei2   

  1. 1- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072
    2- College of Science, Xi'an Shiyou University, Xi'an 710065
  • Received:2015-10-22 Accepted:2016-04-06 Online:2016-10-05 Published:2016-12-15
  • Contact: W. Lv. E-mail address: lvweixiann@163.com
  • Supported by:
    The National Natural Science Foundation of China (11426175); the Foundation of Shaanxi Educational Committee (14JK1578); the Foundation of Xi'an Shiyou University (2014BS14).

Abstract: For a simple digraph $D$, the energy $E(D)$ is defined to be the sum of the absolute values of the real part of all eigenvalues of its adjacent matrix. In this paper, we give a general Coulson-type integral formula for the energy of digraphs by using the method of complex analysis. This integral formula establishes the relationship between the energy and the characteristic polynomial of the digraphs.

Key words: eigenvalues of digraphs, energy of a digraph, Coulson integral formula

CLC Number: