@article{Zhang2025, 
author = {Yuli Zhang and Sizhong Zhou},
title = {An        A          α      -spectral radius for the existence of    {      P    3    ,      P    4    ,      P    5    }-factors in graphs},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {15497-15511},
keywords = {graph, Aα-matrix, Aα-spectral radius, spanning subgraph, {P3, P4, P5}-factor},
url = {https://www.sciopen.com/article/10.3934/math.2025695},
doi = {10.3934/math.2025695},
abstract = {Let    G be a connected graph of order    n with    n  ≥  25. 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          α      -matrix of    G as        A          α        (  G  )  =  α  D  (  G  )  +  (  1  −  α  )  A  (  G  ) [V. Nikiforov, Merging the    A- and    Q-spectral theories, Appl. Anal. Discrete Math., 11 (2017), 81–107], where    α  ∈  [  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          α        (  G  ), denoted by        λ          α        (  G  ), is called the        A          α      -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    ∨  (      K          n      −      2        ∪      K    1    ) if        λ          α        (  G  )  ≥      λ          α        (      K    1    ∨  (      K          n      −      2        ∪      K    1    )  ), where    α is a real number with    0  ≤  α  <      2    3  .}
}