论文标题
$a_α$ - 光谱半径和图形的完美匹配
The $A_α$-spectral radius and perfect matchings of graphs
论文作者
论文摘要
令$α\在[0,1）$中，然后让$ g $是$ n \ geq f（α）$的均匀订单$ n $的图，其中$ f（α）= 10 $ for $ 0 \ 0 \ leqleqα\ leq leq1/2 $，$ f（$ f），$ f（α）= 14 $ for $ 1/2 <α\ leq 2/3 $ f（$ f/3 $ f/） $ 2/3 <α<1 $。在本文中，结果表明，如果$a_α$ - 光度半径为$ g $的半径不小于$ x^3 - （（α + 1）n +α -4）x^2 +（αn^2 +（α^2 -2 -2α-1） $ g $具有完美的匹配，除非$ g = k_1 \ nabla（k_ {n-3} \ cup 2k_1）$。这概括了S. o [光谱半径和图形中的匹配，线性代数应用中的结果。 614（2021）316--324]，它为在邻接光谱半径方面具有完美匹配提供了足够的条件。
Let $α\in[0,1)$, and let $G$ be a graph of even order $n$ with $n\geq f(α)$, where $f(α)=10$ for $0\leq α\leq1/2$, $f(α)=14$ for $1/2<α\leq 2/3$ and $f(α)=5/(1-α)$ for $2/3<α<1$. In this paper, it is shown that if the $A_α$-spectral radius of $G$ is not less than the largest root of $x^3 - ((α+ 1)n +α-4)x^2 + (αn^2 + (α^2 - 2α- 1)n - 2α+1)x -α^2n^2 + (5α^2 - 3α+ 2)n - 10α^2 + 15α- 8=0$ then $G$ has a perfect matching unless $G=K_1\nabla(K_{n-3}\cup 2K_1)$. This generalizes a result of S. O [Spectral radius and matchings in graphs, Linear Algebra Appl. 614 (2021) 316--324], which gives a sufficient condition for the existence of a perfect matching in a graph in terms of the adjacency spectral radius.
