全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用：99美元
投递稿件

查看量下载量

相关文章

更多...

单圈图Sigma指数的极大值
On the Maximum Sigma Index of Unicyclic Graphs

DOI: 10.12677/aam.2025.143114, PP. 276-283

Keywords: Sigma指数，Albertson指数，单圈图
Sigma Index, Albertson Index, Unicyclic Graphs

Full-Text   Cite this paper   Add to My Lib

Abstract:

无向连通图 G 的Sigma指数定义为 σ( G )= ∑ uv∈E( G ) ( d G ( u )？ d G ( v ) ) 2 ，其中， d G ( u ) 和 d G ( v ) 分别表示顶点 u 和 v 在图 G 中的度。本文研究了 n 阶单圈图的Sigma指数，用不同的方法讨论了其最大值。在本文中，我们也得到了单圈图中Sigma指数第二大值，并刻画了其极图。
The sigma of an undirected graph G is defined as σ( G )= ∑ uv∈E( G ) ( d G ( u )？ d G (

References

[1]  Abdo, H. and Dimitrov, D. (2014) The Total Irregularity of Graphs under Graph Operations. Miskolc Mathematical Notes, 15, 3-17.
https://doi.org/10.18514/mmn.2014.593
[2]  Criado, R., Flores, J., García del Amo, A. and Romance, M. (2013) Centralities of a Network and Its Line Graph: An Analytical Comparison by Means of Their Irregularity. International Journal of Computer Mathematics, 91, 304-314.
https://doi.org/10.1080/00207160.2013.793316
[3]  Estrada, E. (2010) Randic Index, Irregularity and Complex Biomolecular Networks. Acta Chimica Slovenica, 57, 597-603.
[4]  Gutman, I., Hansen, P. and Mélot, H. (2005) Variable Neighborhood Search for Extremal Graphs. Comparison of Irregularity Indices for Chemical Trees. Journal of Chemical Information and Modeling, 45, 222-230.
https://doi.org/10.1021/ci0342775
[5]  Reti, T., Sharafdini, R., Dregelyi-Kiss, A. and Haghbin, H. (2018) Graph Irregularity Indices used as Molecular Descriptors in QSPR Studies. MATCH Communications in Mathematical and in Computer Chemistry, 79, 509-524.
[6]  Safaei, F., Tabrizchi, S., Hadian Rasanan, A.H. and Zare, M. (2019) An Energy-Based Heterogeneity Measure for Quantifying Structural Irregularity in Complex Networks. Journal of Computational Science, 36, Article 101011.
https://doi.org/10.1016/j.jocs.2019.06.008
[7]  Albertson, M.O. (1997) The Irregularity of a Graph. ARS Combinatoria, 46, 219-225.
[8]  Bell, F.K. (1992) A Note on the Irregularity of Graphs. Linear Algebra and its Applications, 161, 45-54.
https://doi.org/10.1016/0024-3795(92)90004-t
[9]  Gutman, I., Togan, M., Yurttas, A., Cevik, A.S. and Cangul, I.N. (2018) Inverse Problem for Sigma Index. MATCH Communications in Mathematical and in Computer Chemistry, 79, 491-508.
[10]  Abdo, H., Dimitrov, D. and Gutman, I. (2018) Graphs with Maximal σ Irregularity. Discrete Applied Mathematics, 250, 57-64.
https://doi.org/10.1016/j.dam.2018.05.013
[11]  Réti, T. (2019) On Some Properties of Graph Irregularity Indices with a Particular Regard to the Σ-Index. Applied Mathematics and Computation, 344, 107-115.
https://doi.org/10.1016/j.amc.2018.10.010
[12]  Ali, A., Albalahi, A.M., Alanazi, A.M., Bhatti, A.A. and Hamza, A.E. (2023) On the Maximum Sigma Index of k-Cyclic Graphs. Discrete Applied Mathematics, 325, 58-62.
https://doi.org/10.1016/j.dam.2022.10.009
[13]  Kovijanić Vukićević, Ž., Popivoda, G., Vujošević, S., Škrekovski, R. and Dimitrov, D. (2023) The Σ-Irregularity of Chemical Trees. MATCH Communications in Mathematical and in Computer Chemistry, 91, 267-282.
https://doi.org/10.46793/match.91-1.267k

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133