| Title: | On 2-integral Cayley graphs |
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| Authors: | ID Abdollahi, Alireza (Author)
ID Arezoomand, Majid (Author)
ID Feng, Tao (Author)
ID Wang, Shixin (Author) |
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| Files: |  AMC_Abdollahi,_Arezoomand,_Feng,_Wang_2026.pdf (481,80 KB)
MD5: D8EA13FAF0DAD2A739AC1834224506B7
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | In 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. |
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| Keywords: | Cayley graph, algebraic degree, characters of groups, integral eigenvalue |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 11.06.2026 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 21 str. |
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| Numbering: | Vol. 26, no. 3, [article no.] P3.06 |
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| PID: | 20.500.12556/RUP-23515  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3351.3b6 |
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| Publication date in RUP: | 18.08.2026 |
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| Views: | 30 |
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| Downloads: | 1 |
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