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Graphs with Three Distinct $\alpha$-Eigenvalues
Muhammad Ateeq Tahir
,
Xiao-Dong Zhang
Abstract
In this paper, we investigate properties of graphs with three distinct $\alpha$-eigenvalues of the matrix $A_{\alpha}$. In particular, we show for some $\alpha$ the connected graph $G = K_n − e,$ $G = K_1 \vee (nK_n)$ and some cones over strongly regular graph admit three distinct $\alpha$-eigenvalues.