Resolvent Energy of Digraphs

Document Type : Research Paper

Authors

Department of Mathematics, Qom, Iran

Abstract

In this paper, we present two approaches to compute the resolvent energy of a digraph . The first method computes the energy by ER(G)=\sum_{i=1})^n\frac{1}{n-Re(z_i)}, where Re(z_i )denotes the real part of the eigenvalue z_i of G. In the second method we define ER(G)=\sum_{i=1}^n\frac{1}{n-σ_i}, where σ_i is the ith singular value of G. We prove some properties of resolvent energy for some special digraphs and determine the resolvent energy of unicyclic and bicyclic digraphs and present lower bound for resolvent energy of directed cycles.

Keywords

References

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Iranian Journal of Mathematical Chemistry
Volume 12, Issue 3
September 2021
Pages 139-159

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