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March 6, 2026Filomat0 citationsOpen Access

The existence of a P2, C3, P5, T (3) -factor based on the size or the Aα-spectral radius of graphs

XZX. Y. ZhangLYLihua You

Key Points

  • The aim is to establish conditions under which a specific factor exists in a connected graph based on its spectral radius.
  • Defined connected graphs and their spanning subgraphs.
  • Analyzed the A?-spectral radius for bounds.
  • Constructed extremal graphs to test the lower bound on spectral radius.
  • Identified a lower bound for the size or spectral radius of graphs.
  • Demonstrated that graphs meet this bound can have a {P2, C3, P5, T (3)}-factor.
  • Verified the optimality of the bound with constructed extremal graphs.

Abstract

Let G be a connected graph of order n. A P2, C3, P5, T (3) -factor of G is a spanning subgraph of G such that each component is isomorphic to a member in P2, C3, P5, T (3), where T (3) is a 1, 2, 3-tree. The A? -spectral radius of G is denoted by? ? (G). In this paper, we obtain a lower bound on the size or the A? -spectral radius for? ? [0, 1) of G to guarantee that G has a P2, C3, P5, T (3) -factor, and construct an extremal graph to show that the bound on A? -spectral radius is optimal.

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Cite This Study

Zhang et al. (2025) studied this question.

synapsesocial.com/papers/69aa701a531e4c4a9ff598e5https://doi.org/10.2298/fil2520077z
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