Iota energy orderings of bicyclic signed digraphs

Document Type : Research Paper

Authors

School of Mathematics and Statistics, Northwestern Polytechnical University, 710129, Xi’an, Shaanxi, P. R. China

Abstract

The concept of energy of a signed digraph is extended to iota energy of a signed digraph‎. ‎The energy of a signed digraph $S$ is defined by $E(S)=\sum_{k=1}^n|{Re}(z_k)|$‎, ‎where ${Re}(z_k)$ is the real part of eigenvalue $z_k$ and $z_k$ is the eigenvalue of the adjacency matrix of $S$ with $n$ vertices‎, ‎$k=1, 2,\ldots,n$‎. ‎Then the iota energy of $S$ is defined by $E(S)=\sum_{k=1}^n|{Im}(z_k)|$‎, ‎where ${Im}(z_k)$ is the imaginary part of eigenvalue $z_k$‎. ‎In this paper‎, ‎we consider a special graph class for bicyclic signed digraphs $\mathcal{S}_n$ with $n$ vertices which have two vertex-disjoint signed directed even cycles‎. ‎We give two iota energy orderings of bicyclic signed digraphs‎, ‎one is including two positive or two negative directed even cycles‎, ‎the other is including one positive and one negative directed even cycles‎.

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Main Subjects

References

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Transactions on Combinatorics
Volume 10, Issue 3 - Serial Number 3
September 2021
Pages 187-200

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History

  • Receive Date: 08 January 2021
  • Revise Date: 11 March 2021
  • Accept Date: 24 March 2021
  • Published Online: 01 September 2021

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