Large connected 1-binding even-order graphs have perfect matchings unless they are the join K1 ∨ (K_{n-5} ∪ K3 ∪ K1) when the A_α-spectral radius meets or exceeds that of the exception.
Wu, Some results on thek-strong parity property in a graph, Comput
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Perfect matchings and $A_{\alpha}$-spectral radius in 1-binding graphs
Large connected 1-binding even-order graphs have perfect matchings unless they are the join K1 ∨ (K_{n-5} ∪ K3 ∪ K1) when the A_α-spectral radius meets or exceeds that of the exception.