On Ádám's conjecture for circulant graphs

Mikhail Muzychuk

doi:10.1016/S0012-365X(96)00251-8

On Ádám's conjecture for circulant graphs

Mikhail Muzychuk

Research output: Contribution to journal › Article › peer-review

46 Scopus citations

Abstract

Ádám's (1967) conjecture formulates necessary and sufficient conditions for cyclic (circulant) graphs to be isomorphic. It is known that the conjecture fails if n is divisible by either 8 or by an odd square. On the other hand, it was shown in [?] that the conjecture is true for circulant graphs with square-free number of vertices. In this paper we prove that Ádám's conjecture remains also true if the number of vertices of a graph is twice square-free.

Original language	English
Pages (from-to)	497-510
Number of pages	14
Journal	Discrete Mathematics
Volume	167-168
DOIs	https://doi.org/10.1016/S0012-365X(96)00251-8
State	Published - 15 Apr 1997
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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title = "On {\'A}d{\'a}m's conjecture for circulant graphs",

abstract = "{\'A}d{\'a}m's (1967) conjecture formulates necessary and sufficient conditions for cyclic (circulant) graphs to be isomorphic. It is known that the conjecture fails if n is divisible by either 8 or by an odd square. On the other hand, it was shown in [?] that the conjecture is true for circulant graphs with square-free number of vertices. In this paper we prove that {\'A}d{\'a}m's conjecture remains also true if the number of vertices of a graph is twice square-free.",

author = "Mikhail Muzychuk",

note = "Funding Information: I Partially supported by the Ministry of Science of Israel and by German-Israeli Foundation for Scientific Research and Development.",

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N2 - Ádám's (1967) conjecture formulates necessary and sufficient conditions for cyclic (circulant) graphs to be isomorphic. It is known that the conjecture fails if n is divisible by either 8 or by an odd square. On the other hand, it was shown in [?] that the conjecture is true for circulant graphs with square-free number of vertices. In this paper we prove that Ádám's conjecture remains also true if the number of vertices of a graph is twice square-free.

AB - Ádám's (1967) conjecture formulates necessary and sufficient conditions for cyclic (circulant) graphs to be isomorphic. It is known that the conjecture fails if n is divisible by either 8 or by an odd square. On the other hand, it was shown in [?] that the conjecture is true for circulant graphs with square-free number of vertices. In this paper we prove that Ádám's conjecture remains also true if the number of vertices of a graph is twice square-free.

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DO - 10.1016/S0012-365X(96)00251-8

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AN - SCOPUS:0013552663

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VL - 167-168

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JO - Discrete Mathematics

JF - Discrete Mathematics

ER -

On Ádám's conjecture for circulant graphs

Abstract

ASJC Scopus subject areas

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