Generalized Connectivity of the Mycielskian Graph under g-Extra Restriction
Abstract
:1. Introduction
2. Terminology and Notations
3. Main Results
- (1)
- If there exists some such that , then ( be the twin of F) is disconnected and the smallest component is the isolated vertex .
- (2)
- If for any , then is connected to in (where and be the twin of and F, respectively).
- (3)
- If there exists one vertex w such that and , then is disconnected and ( is the twin of w) is an isolated vertex.
- (2)
- In this situation, for any , there exists one edge . By the construction of , and (see Figure 2b). Then is connected to in .
- (3)
- In this situation, there exists one vertex w such that and . By the construction of , is the twin of w, and (see Figure 2c). Then is disconnected and is an isolated vertex.
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Zou, J.; Li, H.; Zhang, S.; Ye, C. Generalized Connectivity of the Mycielskian Graph under g-Extra Restriction. Mathematics 2023, 11, 4043. https://doi.org/10.3390/math11194043
Zou J, Li H, Zhang S, Ye C. Generalized Connectivity of the Mycielskian Graph under g-Extra Restriction. Mathematics. 2023; 11(19):4043. https://doi.org/10.3390/math11194043
Chicago/Turabian StyleZou, Jinyu, He Li, Shumin Zhang, and Chengfu Ye. 2023. "Generalized Connectivity of the Mycielskian Graph under g-Extra Restriction" Mathematics 11, no. 19: 4043. https://doi.org/10.3390/math11194043
APA StyleZou, J., Li, H., Zhang, S., & Ye, C. (2023). Generalized Connectivity of the Mycielskian Graph under g-Extra Restriction. Mathematics, 11(19), 4043. https://doi.org/10.3390/math11194043