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Construction for a Class of Borderenergetic Digraphs

Received: 10 October 2022     Accepted: 28 October 2022     Published: 4 November 2022
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Abstract

The energy of a digraph is defined as the sum of all real parts of its eigenvalues which are respect to its adjacency matrix. It is well known that graph energy is found that there are many applications in chemistry, physics and biology. In 2015, Gong and Gutman et al. proposed the concept of a borderenergetic graph. That is, if a graph G of order n satisfies its graph energy is equal to the value obtained by using twice of its order minus two, then G is called a borderenergetic graph. That is, the energies of borderenergetic graphs are equal to those of complete graphs of the same orders. Note that a graph is also a special digraph. Naturally, the concept of a borderenergetic digraph is extended to digraph energy. In this work, we first characterize its matrix and obtain the relationship between the spectra of a digraph and its complement. By using the spectra of the complete product between two regular digraphs, a kind of borderenergetic digraphs can be constructed. Furthermore, based on the results before, a class of sequences of borderenergetic digraphs can be constructed.

Published in Mathematics and Computer Science (Volume 7, Issue 5)
DOI 10.11648/j.mcs.20220705.12
Page(s) 102-105
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Regular Digraphs, Spectrum of a Digraph, Digraph Energy, Borderenergetic Digraphs

References
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[3] K. C. Das, S. A. Mojallal, Upper Bounds for the Energy of Graphs. MAT-CH Commun. Math. Comput. Chem. 70 (2013) 657-662.
[4] B. Deng, I. Gutman, X. Li, More on borderenergetic graphs. Linear Algeb-ra and its Applications. 497 (2016) 199-208.
[5] B. Deng, X. Li, Energies for the complements of borderenergetic graphs. MATCH Commun. Math. Comput. Chem. 85 (2021) 181-194.
[6] B. Deng, W. Liang, X. Lu, N. Yang, Digraph Energy of Directed Polygons. Combinatorial Chemistry & High Throughput Screening, 25 (2022) 496-499.
[7] B. Furtula, I. Gutman, Borderenergetic graphs of order 12. Journal of Mat-hematical Chemistry. (2017) 339-344.
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[9] S. C. Gong, X. Li, G. H. Xu, I. Gutman, B. Furtula, Borderenergetic gra-phs. MATCH Commun. Math. Comput. Chem. 74 (2015) 321–332.
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[11] E. Gudiño, J. Rada, A lower bound for the spectral radius of a digraph. Linear Algebra and its Applications. 433 (2010) 233-240.
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[18] W. López, J. Rada, Equienergetic digraphs. International journal of pure and applied mathematics. 36 (2007) 361-372.
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  • APA Style

    Xumei Jin, Bo Deng, Hongyu Zhang. (2022). Construction for a Class of Borderenergetic Digraphs. Mathematics and Computer Science, 7(5), 102-105. https://doi.org/10.11648/j.mcs.20220705.12

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    ACS Style

    Xumei Jin; Bo Deng; Hongyu Zhang. Construction for a Class of Borderenergetic Digraphs. Math. Comput. Sci. 2022, 7(5), 102-105. doi: 10.11648/j.mcs.20220705.12

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    AMA Style

    Xumei Jin, Bo Deng, Hongyu Zhang. Construction for a Class of Borderenergetic Digraphs. Math Comput Sci. 2022;7(5):102-105. doi: 10.11648/j.mcs.20220705.12

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  • @article{10.11648/j.mcs.20220705.12,
      author = {Xumei Jin and Bo Deng and Hongyu Zhang},
      title = {Construction for a Class of Borderenergetic Digraphs},
      journal = {Mathematics and Computer Science},
      volume = {7},
      number = {5},
      pages = {102-105},
      doi = {10.11648/j.mcs.20220705.12},
      url = {https://doi.org/10.11648/j.mcs.20220705.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20220705.12},
      abstract = {The energy of a digraph is defined as the sum of all real parts of its eigenvalues which are respect to its adjacency matrix. It is well known that graph energy is found that there are many applications in chemistry, physics and biology. In 2015, Gong and Gutman et al. proposed the concept of a borderenergetic graph. That is, if a graph G of order n satisfies its graph energy is equal to the value obtained by using twice of its order minus two, then G is called a borderenergetic graph. That is, the energies of borderenergetic graphs are equal to those of complete graphs of the same orders. Note that a graph is also a special digraph. Naturally, the concept of a borderenergetic digraph is extended to digraph energy. In this work, we first characterize its matrix and obtain the relationship between the spectra of a digraph and its complement. By using the spectra of the complete product between two regular digraphs, a kind of borderenergetic digraphs can be constructed. Furthermore, based on the results before, a class of sequences of borderenergetic digraphs can be constructed.},
     year = {2022}
    }
    

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    AU  - Xumei Jin
    AU  - Bo Deng
    AU  - Hongyu Zhang
    Y1  - 2022/11/04
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    N1  - https://doi.org/10.11648/j.mcs.20220705.12
    DO  - 10.11648/j.mcs.20220705.12
    T2  - Mathematics and Computer Science
    JF  - Mathematics and Computer Science
    JO  - Mathematics and Computer Science
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    PB  - Science Publishing Group
    SN  - 2575-6028
    UR  - https://doi.org/10.11648/j.mcs.20220705.12
    AB  - The energy of a digraph is defined as the sum of all real parts of its eigenvalues which are respect to its adjacency matrix. It is well known that graph energy is found that there are many applications in chemistry, physics and biology. In 2015, Gong and Gutman et al. proposed the concept of a borderenergetic graph. That is, if a graph G of order n satisfies its graph energy is equal to the value obtained by using twice of its order minus two, then G is called a borderenergetic graph. That is, the energies of borderenergetic graphs are equal to those of complete graphs of the same orders. Note that a graph is also a special digraph. Naturally, the concept of a borderenergetic digraph is extended to digraph energy. In this work, we first characterize its matrix and obtain the relationship between the spectra of a digraph and its complement. By using the spectra of the complete product between two regular digraphs, a kind of borderenergetic digraphs can be constructed. Furthermore, based on the results before, a class of sequences of borderenergetic digraphs can be constructed.
    VL  - 7
    IS  - 5
    ER  - 

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Author Information
  • School of Mathematics and Statistics, Qinghai Normal University, Xining, China

  • School of Mathematics and Statistics, Qinghai Normal University, Xining, China

  • School of Mathematics and Statistics, Qinghai Normal University, Xining, China

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