| dc.contributor.author | Yuli Zhang | |
| dc.contributor.author | Sizhong Zhou | |
| dc.contributor.other | School of Science, Dalian Jiaotong University, Dalian, Liaoning 116028, China | |
| dc.contributor.other | School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, China | |
| dc.date.accessioned | 2025-08-27T02:32:32Z | |
| dc.date.accessioned | 2025-10-08T09:10:15Z | |
| dc.date.available | 2025-10-08T09:10:15Z | |
| dc.date.issued | 01-07-2025 | |
| dc.identifier.uri | https://www.aimspress.com/article/doi/10.3934/math.2025695 | |
| dc.identifier.uri | http://digilib.fisipol.ugm.ac.id/repo/handle/15717717/39141 | |
| dc.description.abstract | Let $ G $ be a connected graph of order $ n $ with $ n\geq25 $. A $ \{P_3, P_4, P_5\} $-factor is a spanning subgraph $ H $ of $ G $ such that every component of $ H $ is isomorphic to an element of $ \{P_3, P_4, P_5\} $. Nikiforov introduced the $ A_{\alpha} $-matrix of $ G $ as $ A_{\alpha}(G) = \alpha D(G)+(1-\alpha)A(G) $ [V. Nikiforov, Merging the $ A $- and $ Q $-spectral theories, Appl. Anal. Discrete Math., 11 (2017), 81–107], where $ \alpha\in[0, 1] $, $ D(G) $ denotes the diagonal matrix of vertex degrees of $ G $ and $ A(G) $ denotes the adjacency matrix of $ G $. The largest eigenvalue of $ A_{\alpha}(G) $, denoted by $ \lambda_{\alpha}(G) $, is called the $ A_{\alpha} $-spectral radius of $ G $. In this paper, it is proved that $ G $ has a $ \{P_3, P_4, P_5\} $-factor unless $ G = K_1\vee(K_{n-2}\cup K_1) $ if $ \lambda_{\alpha}(G)\geq\lambda_{\alpha}(K_1\vee(K_{n-2}\cup K_1)) $, where $ \alpha $ is a real number with $ 0\leq\alpha < \frac{2}{3} $. | |
| dc.language.iso | EN | |
| dc.publisher | AIMS Press | |
| dc.subject.lcc | Mathematics | |
| dc.title | An $ A_{\alpha} $-spectral radius for the existence of $ \{P_3, P_4, P_5\} $-factors in graphs | |
| dc.type | Article | |
| dc.description.keywords | graph | |
| dc.description.keywords | $ a_{\alpha} $-matrix | |
| dc.description.keywords | $ a_{\alpha} $-spectral radius | |
| dc.description.keywords | spanning subgraph | |
| dc.description.keywords | $ \{p_3, p_4, p_5\} $-factor | |
| dc.description.pages | 15497-15511 | |
| dc.description.doi | 10.3934/math.2025695 | |
| dc.title.journal | AIMS Mathematics | |
| dc.identifier.e-issn | 2473-6988 | |
| dc.identifier.oai | oai:doaj.org/journal:c3f2affbbdd94fcab6351e393da0e9c1 | |
| dc.journal.info | Volume 10, Issue 7 | |
