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 |
Regular Digraphs, Spectrum of a Digraph, Digraph Energy, Borderenergetic Digraphs
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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
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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Download@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}
}
TY - JOUR T1 - Construction for a Class of Borderenergetic Digraphs AU - Xumei Jin AU - Bo Deng AU - Hongyu Zhang Y1 - 2022/11/04 PY - 2022 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 SP - 102 EP - 105 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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