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Graphs with Three Distinct $α$ -Eigenvalues

Muhammad Ateeq Tahir , $icon-email$ Xiao-Dong Zhang

Abstract

In this paper, we investigate properties of graphs with three distinct $α$ -eigenvalues of the matrix $A_{α}$ . In particular, we show for some $α$ the connected graph $G = K_{n} - e,$ $G = K_{1} \lor (n K_{n})$ and some cones over strongly regular graph admit three distinct $α$ -eigenvalues.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Mã bưu điện: 10072

Viện Hàn lâm Khoa học và Công nghệ Việt Nam Hội Toán học Việt Nam Viện Nghiên cứu Cao cấp về toán

Acta Mathematica Vietnamica

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Graphs with Three Distinct α-Eigenvalues

Abstract

Graphs with Three Distinct $α$ -Eigenvalues