التفاصيل البيبلوغرافية
| العنوان: |
Generalized Connectivity of the Mycielskian Graph under g-Extra Restriction |
| المؤلفون: |
Jinyu Zou, He Li, Shumin Zhang, Chengfu Ye |
| المصدر: |
Mathematics, Vol 11, Iss 19, p 4043 (2023) |
| بيانات النشر: |
MDPI AG, 2023. |
| سنة النشر: |
2023 |
| المجموعة: |
LCC:Mathematics |
| مصطلحات موضوعية: |
connectivity, g-extra connectivity, Mycielskian graph, Mathematics, QA1-939 |
| الوصف: |
The g-extra connectivity is a very important index to evaluate the fault tolerance, reliability of interconnection networks. Let g be a non-negative integer, G be a connected graph with vertex set V and edge set E, a subset S⊆V is called a g-extra cut of G if the graph induced by the set G−S is disconnected and each component of G−S has at least g+1 vertices. The g-extra connectivity of G, denoted as κg(G), is the cardinality of the minimum g-extra cut of G. Mycielski introduced a graph transformation to discover chromatic numbers of triangle-free graphs that can be arbitrarily large. This transformation converts a graph G into a new compound graph called μ(G), also known as the Mycielskian graph of G. In this paper, we study the relationship on g-extra connectivity between the Mycielskian graph μ(G) and the graph G. In addition, we show that κ3(μ(G))=2κ1(G)+1 for κ1(G)≤min{4,⌊n2⌋}, and prove the bounds of κ2g+1(μ(G)) for g≥2. |
| نوع الوثيقة: |
article |
| وصف الملف: |
electronic resource |
| اللغة: |
English |
| تدمد: |
2227-7390 |
| Relation: |
https://www.mdpi.com/2227-7390/11/19/4043; https://doaj.org/toc/2227-7390 |
| DOI: |
10.3390/math11194043 |
| URL الوصول: |
https://doaj.org/article/229d40186b554c9aaf507eeb9fd10da8 |
| رقم الانضمام: |
edsdoj.229d40186b554c9aaf507eeb9fd10da8 |
| قاعدة البيانات: |
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