Bazı Graf Sınıflarında 1-Düzenli ve 2-Düzenli Ayrıt Bağlantılılık

Yıl 2023, Cilt: 6 Sayı: Ek Sayı, 415 - 425, 20.12.2023

İdris Çiftçi

https://doi.org/10.47495/okufbed.1211664

Öz

Düzenli ayrıt bağlantılılık yeni bir koşullu bağlantılılık türü olup, bu kavram bağlantısız yapılan her parça grafın düzenli olması esasına dayanır. Bu çalışmada, hiperküp graflarında ve bir tam grafın yol, çevre ve bir tam grafla kartezyen çarpımından elde edilen graflarda 1-düzenli ve 2-düzenli ayrıt bağlantılılık incelenmiştir.

Anahtar Kelimeler

Bağlantılılık, Koşullu Bağlantılılık, Ayrıt Bağlantılılık, Düzenli Ayrıt Bağlantılılık, 1-Düzenli Ayrıt Bağlantılılık, 2-Düzenli Ayrıt Bağlantılılık, Connectivity, Conditional Connectivity, Edge Connectivity, Regular Edge Connectivity, 1-Regular Edge Connectivity, 2-Regular Edge Connectivity

On 1-Regular and 2- Regular Edge Connectivity in Some Graph Classes

Öz

Regular edge connectivity is a new type of conditional connectivity, and this concept is based on the regularity of every disconnected component graphs. In this study, 1-regular and 2-regular edge connectivity were investigated in hypercube graphs and graphs obtained from path, cycle and complete graphs with Cartesian product a complete graph.

Anahtar Kelimeler

Connectivity, Conditional Connectivity, Edge Connectivity, Regular Edge Connectivity, 1-Regular Edge Connectivity, 2-Regular Edge Connectivity

Kaynakça

• Balbuena C., Marcote X. The p-restricted edge-connectivity of Kneser graphs. Applied Mathematics and Computation 2019; 343: 258-267.
• Deo N. Graph Theory with applications to engineering and computer science. Courier Dover Publications; 2017. Diestel R. Grapht theory. Springer Science & Business Media. 2005.
• Ediz S., Çiftçi İ. On k-regular edge connectivity of chemical graphs. Main Group Metal Chemistry 2022; 45(1): 106-110.
• Fabrega J., Fiol MA. On the extraconnectivity of graphs. Discrete Mathematics 1996; 155: 49–57.
• Guo L., Zhang M., Zhai S., Xu L. Relation of extra edge connectivity and component edge connectivity for regular Networks. International Journal of Foundations of Computer Science 2021; 32(2): 137–149.
• Hao RX., Tian ZX., Xu JM. Relationship between conditional diagnosability and 2-extra connectivity of symmetric graphs. Theoretical Computer Science 2016; 627: 36-53.
• Harary F. Conditional connectivity. Networks 1983; 13(3): 347–357.
• Latifi S., Hegde M., Naraghipour M. Conditional connectivity measures for large multiprocessor systems. IEEE Transactions on Computers 1994; 43: 218–222.
• Li H., Yang W. Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes. Discrete Applied Mathematics 2013; 161(16-17): 2753-2757.
• Li P., Xu M. Fault-tolerant strong Menger (edge) connectivity and 3-extra edge-connectivity of balanced hypercubes. Theoretical Computer Science 2018; 707: 56-68.
• Li X., Lin CK., Fan J., Jia X., Cheng B., Zhou J. Relationship between extra connectivity and component connectivity ın networks. The Computer Journal 2021; 64(1): 38–53.
• Lin L., Huang Y., Wang X., Xu L. Restricted connectivity and good-neighbor diagnosability of split-star networks. Theoretical Computer Science 2020; 824: 81-91.
• Liu X., Meng J. The k-restricted edge-connectivity of the data center network DCell. Applied Mathematics and Computation 2021; 396: 125941.
• Lü H. On extra connectivity and extra edge-connectivity of balanced hypercubes. International Journal of Computer Mathematics 2017; 94(4): 813-820.