University of Isfahan Transactions on Combinatorics 2251-8657 10 3 2021 09 01 Iota energy orderings of bicyclic signed digraphs 187 200 25567 10.22108/toc.2021.126881.1805 EN Xiuwen Yang School of Mathematics and Statistics, Northwestern Polytechnical University, 710129, Xi’an, Shaanxi, P. R. China Ligong Wang School of Mathematics and Statistics, Northwestern Polytechnical University, 710129, Xi’an, Shaanxi, P. R. China Journal Article 2021 01 08 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. https://toc.ui.ac.ir/article_25567_b7b94ad4ded8b3949671f85716761580.pdf