Research article
On energy ordering of vertex-disjoint bicyclic sidigraphs
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School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, Pakistan
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Received:
09 March 2020
Accepted:
13 July 2020
Published:
28 August 2020
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MSC :
05C35, 05C50
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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 $n$.
Citation: Sumaira Hafeez, Rashid Farooq. On energy ordering of vertex-disjoint bicyclic sidigraphs[J]. AIMS Mathematics, 2020, 5(6): 6693-6713. doi: 10.3934/math.2020430
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Abstract
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 $n$.
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