Iota energy orderings of bicyclic signed digraphs

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=۱}^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=۱, ۲,\ldots,n‎. ‎Then the iota energy of S is defined by E(S)=\sum_{k=۱}^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.

کلیدواژه ها:

‎Orderings‎ ، ‎iota energy‎ ، ‎bicyclic signed digraphs