| Autor: |
Jinyu Zou, He Li, Shumin Zhang, Chengfu Ye |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Mathematics, Vol 11, Iss 19, p 4043 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2227-7390 |
| DOI: |
10.3390/math11194043 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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