On So's conjecture for integral circulant graphs | Zendy

J. Sander | Zendy; Torsten Sander | Zendy

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On So's conjecture for integral circulant graphs

Author(s) -

J. Sander,

Torsten Sander

Publication year - 2015

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm150226009s

Subject(s) - mathematics , circulant matrix , conjecture , combinatorics , vertex (graph theory) , circulant graph , eigenvalues and eigenvectors , multiplicative function , isospectral , order (exchange) , divisor (algebraic geometry) , discrete mathematics , graph , pure mathematics , mathematical analysis , line graph , physics , finance , voltage graph , quantum mechanics , economics

Each integral circulant graph ICG(n,D) is characterised by its order n and a set D of positive divisors of n in such a way that it has vertex set Z=nZ and edge set {(a,b) : a, b Z=nZ, gcd(a - b,n) D}. According to a conjecture of So two integral circulant graphs are isomorphic if and only if they are isospectral, i.e. they have the same eigenvalues (counted with multiplicities). We prove a weaker form of this conjecture, namely, that two integral circulant graphs with multiplicative divisor sets are isomorphic if and only if their spectral vectors coincide.

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