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), 2024. Published by Science Publishing Group |
Regular Digraphs, Spectrum of a Digraph, Digraph Energy, Borderenergetic Digraphs
| [1] | J. R. Carmona, J. Rodríguez, On the spectral radius and energy of digraphs. Linear and Multilinear Algebra. (2021) 1-12. |
| [2] | S. Y. Cui, G. X. Tian, On upper bounds for the energy of digraphs. Linear Algebra and its Applications. 438 (2013) 4742-4749. |
| [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. |
| [8] | S. Gong, X. Li, M. Wei, A Computer Search for the Borderenergetic Grap-hs of Order 10. MATCH Commun. Math. Comput. Chem. 74 (2015) 333-342. |
| [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. |
| [10] | E. Gudiño, I. Gutman, D. Quiroz, Upper bound for the energy of graphs with fixed second and fourth spectral moments. Kragujevac Journal of Mat-hematics. 32 (2009) 27-35. |
| [11] | E. Gudiño, J. Rada, A lower bound for the spectral radius of a digraph. Linear Algebra and its Applications. 433 (2010) 233-240. |
| [12] | I. Gutman, The energy of a graph. Ber. Math-Statist. Sekt. Forschungszentrum. Graz. 103 (1978) 1-22. |
| [13] | I. Gutman, The energy of a graph. Discrete Applied Mathematics. 160 (2012) 2177-2187. |
| [14] | I. Gutman, X. Li, Y. Shi, Graph Energy. Springer, New York, 2012. |
| [15] | I. Gutman, O. E. Polansky, Mathematical concepts in organic chemistry. Springer, Berlin, Germany, 1986. |
| [16] | Y. Hou, Q. Tao, Borderenergetic threshold graphs. MATCH Commun. Math. Comput. Chem. 75 (2016) 253-262. |
| [17] | H. Liu, M. Lu, F. Tian, Some upper bounds for the energy of graphs. Journal of Mathematical Chemistry. 41 (2007) 45-57. |
| [18] | W. López, J. Rada, Equienergetic digraphs. International journal of pure and applied mathematics. 36 (2007) 361-372. |
| [19] | B. Mohar, Eigenvalues and colorings of digraphs. Linear Algebra and its Applications. 432 (2010) 2273-2277. |
| [20] | J. Monsalve, J. Rada, Energy of strongly connected digraphs whose underlying graph is a cycle. Proyecciones. 35 (2016) 395-404. |
| [21] | V. Nikiforov, The Energy of Graphs and Matrices, Journal of Mathematical analysis and applications. 326 (2007) 1472-1475. |
| [22] | I. Pena, J. Rada, Energy of digraphs. Linear and Multilinear Algebra. 56 (2008) 565-579. |
| [23] | J. Rada, Lower bounds for the energy of digraphs. Linear Algebra and its Applications. 432 (2010) 2174-2180. |
| [24] | J. Rada, The McClelland inequality for the energy of digraphs. Linear Algebra and its Applications. 430 (2009) 800-804. |
| [25] | A. B. Richard, Spectra of digraphs. Linear Algebra and its Applications. 432 (2010) 2181-2213. |
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
Share This Article
Twitter
Linked In
Facebook
Copy
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 -
Email: