On 2-integral Cayley graphsAbdollahi, Alireza (Avtor) Arezoomand, Majid (Avtor) Feng, Tao (Avtor) Wang, Shixin (Avtor) Cayley graphalgebraic degreecharacters of groupsintegral eigenvalueIn this paper, we introduce the concept of k-integral graphs. A graph Γ is called k-integral if the extension degree of the splitting field of the characteristic polynomial of Γ over rational field ℚ is equal to k. We prove that for any positive integers k and Δ, the set of all finite connected graphs with algebraic degree at most k and maximum degree at most Δ is finite. We study 2-integral Cayley graphs over finite groups G with respect to Cayley sets which are a union of conjugacy classes of G. Among other general results, we completely characterize all finite abelian groups having a connected 2-integral Cayley graph with valency 2, 3, 4 and 5. Furthermore, we classify the finite groups G that al Cayley graphs over G with bounded valency are 2-integral.Založba Univerze na Primorskem20262026-08-18 10:57:54Članek v reviji23515UDK: 51eISSN: 1855-3974DOI: 10.26493/1855-3974.3351.3b6sl