On energy ordering of vertex-disjoint bicyclic sidigraphs

• Main Authors: Sumaira Hafeez, Rashid Farooq
• Format: Article
• Language: English
• Published: AIMS Press 2020-09-01
• Series: AIMS Mathematics
• Subjects: signed digraphs; energy ordering; maximal energy
• Online Access: https://www.aimspress.com/article/10.3934/math.2020430/fulltext.html

The energy and iota energy of signed digraphs are respectively defined by $E(S)=$ $\sum_{k=1}^n|{\rm Re}(\rho_k)|$ and $E_c(S)=\sum_{k=1}^n|{\rm Im }(\rho_k)|$, where $\rho_1, \dots,\rho_n$ are eigenvalues of $S$, and ${\rm Re}(\rho_k)$ and ${\rm Im}(\rho_k)$ are respectively real and imaginary values of the eigenvalue $\rho_k$. Recently, Yang and Wang (2018) found the energy and iota energy ordering of digraphs in $\mathcal{D}_n$ and computed the maximal energy and iota energy, where $\mathcal{D}_n$ denotes the set of vertex-disjoint bicyclic digraphs of a fixed order $n$. In this paper, we investigate the energy ordering of signed digraphs in $\mathcal{D}_n^s$ and find the maximal energy, where $\mathcal{D}_n^s$ denotes the set of vertex-disjoint bicyclic sidigraphs of a fixed order $n$.