In this paper, we introduce the concept of k-integral graphs. A graph ? is called k-integral if the extension degree of the splitting field of the characteristic polynomial of ? over rational field Q is equal to k. We prove that for any positive integers k and ?, the set of all finite connected graphs with algebraic degree at most k and maximum degree at most ? 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.

Rights

URN

URN:NBN:SI:DOC-O9PGQOKQ

COBISSID

289903363

DOI

10.26493/1855-3974.3351.3b6

Added

27.10.2026

Metadata

Citation

APA:

Abdollahi, Alireza, Arezoomand, Majid, Feng, Tao, Wang, Shixin (2026). On 2-integral Cayley graphs. Ars mathematica contemporanea, volume 26, issue 3, article p3.06, str. 1-21. URN:NBN:SI:DOC-O9PGQOKQ from http://www.dlib.si

MLA:

Abdollahi, Alireza, Arezoomand, Majid, Feng, Tao, Wang, Shixin. "On 2-integral Cayley graphs." Ars mathematica contemporanea volume 26. issue 3. article p3.06 (2026) str. 1-21.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-O9PGQOKQ>