Research article

On energy ordering of vertex-disjoint bicyclic sidigraphs

  • Received: 09 March 2020 Accepted: 13 July 2020 Published: 28 August 2020
  • MSC : 05C35, 05C50

  • 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

    Related Papers:

  • 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 $n$.


    加载中


    [1] I. Peña, J. Rada, Energy of digraphs, Linear Multilinear A., 56 (2008), 565-579. doi: 10.1080/03081080701482943
    [2] S. Pirzada, M. A. Bhat, Energy of signed digraphs, Discrete Appl. Math., 169 (2014), 195-205. doi: 10.1016/j.dam.2013.12.018
    [3] M. Khan, R. Farooq, J. Rada, Complex adjacency matrix and energy of digraphs, Linear Multilinear A., 65 (2017), 2170-2186. doi: 10.1080/03081087.2016.1265064
    [4] R. Farooq, M. Khan, S. Chand, On iota energy of signed digraphs, Linear Multilinear A., 67 (2019), 705-724. doi: 10.1080/03081087.2018.1431200
    [5] M. Khan, R. Farooq, On the energy of bicyclic signed digraphs, J. Math. Inequal., 11 (2017), 845-862 .
    [6] M. Khan, R. Farooq, A. A. Siddiqui, On the extremal energy of bicyclic digraphs, J. Math. Inequal., 9 (2015), 799-810.
    [7] R. Farooq, M. Khan, F. Ahmad, Extremal iota energy of bicyclic digraphs, Appl. Math. Comput., 303 (2017), 24-33.
    [8] R. Farooq, S. Chand, M. Khan, Iota energy of bicyclic signed digraphs, Asian-European J. Math., 12 (2019), 1-14.
    [9] J. Monslave, J. Rada, Bicyclic digraphs with maximal energy, Appl. Math. Comput., 280 (2016), 124-131.
    [10] S. Hafeez, R. Farooq, M. Khan, Bicylic signed digraphs with maximal energy, Appl. Math. Comput., 347 (2019), 702-711.
    [11] X. Yang, L. Wang, On the ordering of bicyclic digraphs with respect to energy and iota energy, Appl. Math. Comput., 339 (2018), 768-778.
    [12] X. Yang, L. Wang, Ordering of bicyclic signed digraphs by energy, Filomat, to appear.
    [13] X. Yang, L. Wang, Iota energy ordering of bicyclic signed digraphs, arXiv:2004.01412v1.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2673) PDF downloads(75) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog