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The $A_{\\alpha}$-characteristic polynomial of $G$ is defined to be $$ \\det(xI_n-A_{\\alpha}(G))=\\sum_jc_{\\alpha j}(G)x^{n-j}, $$ where $\\det(*)$ denotes the determinant of $*$, and $I_n$ is the identity matrix of size $n$. The $A_{\\alpha}$-spectrum of $G$ consists of all roots of the $A_{\\alpha}$-characteristic polynomial of $G$. 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Define $$ A_{\\alpha}(G)=\\alpha D(G)+(1-\\alpha)A(G) $$ for any real $\\alpha\\in [0,1]$. The $A_{\\alpha}$-characteristic polynomial of $G$ is defined to be $$ \\det(xI_n-A_{\\alpha}(G))=\\sum_jc_{\\alpha j}(G)x^{n-j}, $$ where $\\det(*)$ denotes the determinant of $*$, and $I_n$ is the identity matrix of size $n$. The $A_{\\alpha}$-spectrum of $G$ consists of all roots of the $A_{\\alpha}$-characteristic polynomial of $G$. 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