Remarks on path-factor critical avoidable graphs
Zhou (2023) introduced the concept of path-factor critical avoidable graph and determined several parameter bounds for (P≥2,n) or (P≥3,n)-factor critical avoidable graphs. Certain instances are listed in Zhou (2023) to show that these toughness or isolated toughness bounds are sharp. However, the de...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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KeAi Communications Co., Ltd.
2023-06-01
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| Series: | International Journal of Cognitive Computing in Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666307423000074 |
| _version_ | 1797377834538237952 |
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| author | Zhengyue He Li Liang Haci Mehmet Baskonus Wei Gao |
| author_facet | Zhengyue He Li Liang Haci Mehmet Baskonus Wei Gao |
| author_sort | Zhengyue He |
| collection | DOAJ |
| description | Zhou (2023) introduced the concept of path-factor critical avoidable graph and determined several parameter bounds for (P≥2,n) or (P≥3,n)-factor critical avoidable graphs. Certain instances are listed in Zhou (2023) to show that these toughness or isolated toughness bounds are sharp. However, the derivation processes are flawed. In this remark, we directly modify the derivation processes and obtain the revised bounds. The counterexamples are updated to satisfy κ(G)=n+2. Finally, richness bounds on binding number for a graph to be path-factor critical avoidable are determined. |
| first_indexed | 2024-03-08T19:58:01Z |
| format | Article |
| id | doaj.art-4eca7ae217934f26825617a33c759e55 |
| institution | Directory Open Access Journal |
| issn | 2666-3074 |
| language | English |
| last_indexed | 2024-03-08T19:58:01Z |
| publishDate | 2023-06-01 |
| publisher | KeAi Communications Co., Ltd. |
| record_format | Article |
| series | International Journal of Cognitive Computing in Engineering |
| spelling | doaj.art-4eca7ae217934f26825617a33c759e552023-12-24T04:46:37ZengKeAi Communications Co., Ltd.International Journal of Cognitive Computing in Engineering2666-30742023-06-0146570Remarks on path-factor critical avoidable graphsZhengyue He0Li Liang1Haci Mehmet Baskonus2Wei Gao3School of Information Science and Technology, Yunnan Normal University, Kunming 650500, ChinaSchool of Information Science and Technology, Yunnan Normal University, Kunming 650500, ChinaDepartment of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa 63050, TurkeyCorresponding author.; School of Information Science and Technology, Yunnan Normal University, Kunming 650500, ChinaZhou (2023) introduced the concept of path-factor critical avoidable graph and determined several parameter bounds for (P≥2,n) or (P≥3,n)-factor critical avoidable graphs. Certain instances are listed in Zhou (2023) to show that these toughness or isolated toughness bounds are sharp. However, the derivation processes are flawed. In this remark, we directly modify the derivation processes and obtain the revised bounds. The counterexamples are updated to satisfy κ(G)=n+2. Finally, richness bounds on binding number for a graph to be path-factor critical avoidable are determined.http://www.sciencedirect.com/science/article/pii/S266630742300007405C7005C38 |
| spellingShingle | Zhengyue He Li Liang Haci Mehmet Baskonus Wei Gao Remarks on path-factor critical avoidable graphs International Journal of Cognitive Computing in Engineering 05C70 05C38 |
| title | Remarks on path-factor critical avoidable graphs |
| title_full | Remarks on path-factor critical avoidable graphs |
| title_fullStr | Remarks on path-factor critical avoidable graphs |
| title_full_unstemmed | Remarks on path-factor critical avoidable graphs |
| title_short | Remarks on path-factor critical avoidable graphs |
| title_sort | remarks on path factor critical avoidable graphs |
| topic | 05C70 05C38 |
| url | http://www.sciencedirect.com/science/article/pii/S2666307423000074 |
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