Two kinds of conditional connectivity of hypercubes
| Autor: | Bo Zhu, Shumin Zhang, Jinyu Zou, Chengfu Ye |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | AKCE International Journal of Graphs and Combinatorics, Vol 19, Iss 3, Pp 255-260 (2022) |
| Druh dokumentu: | article |
| ISSN: | 09728600 2543-3474 0972-8600 |
| DOI: | 10.1080/09728600.2022.2132893 |
| Popis: | AbstractA subset [Formula: see text] is called an h-extra r-component cut of G if G – F is disconnected and there are at least r components, each component has at least h + 1 vertices. The cardinality of a minimum h-extra r-component cut of G, denoted by [Formula: see text] is the h-extra r-component connectivity of G. In this paper, we introduce a novel connectivity called the g-good r-component connectivity. For [Formula: see text] if G – F is disconnected and there are at least r components and each vertex [Formula: see text] has at least g neighbors, then F is called a g-good r-component cut of G; the g-good r-component connectivity of G, denoted by [Formula: see text] is the minimum cardinality of a g-good r-component cut of G. In this work, we prove that [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text] where Qn is n-dimension hypercube. |
| Databáze: | Directory of Open Access Journals |
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