A solution of the isomorphism problem for circulant graphs

Muzychuk, Mikhail

doi:10.1112/s0024611503014412

Cited by 93 publications

(75 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It also allows for building the mapping function in linear time. The overall complexity of the method compares favorably with the known results (see Muzychuk 2004).…”

Section: The Isomorphism and Coloring Problems On Circulant Graphssupporting

confidence: 70%

Some classical combinatorial problems on circulant and claw-free graphs: the isomorphism and coloring problems on circulant graphs and the stable set problem on claw-free graphs

Pietropaoli

2008

4OR-Q J Oper Res

View full text Add to dashboard Cite

This is a summary of the author's Ph.D. thesis supervised by Sara Nicoloso and Gianpaolo Oriolo and defended on 3 April 2008 at Sapienza UniversitA di Roma. The thesis is written in English and is available from the author upon request. This work deals with three classical combinatorial problems, namely the isomorphism, the vertex-coloring and the stable set problem, restricted to two graph classes, namely circulant and claw-free graphs. In the first part (joint work with Sara Nicoloso), we derive a necessary and sufficient condition to test isomorphism of circulant graphs, and give simple algorithms to solve the vertex-coloring problem on this class of graphs. In the second part (joint work with Gianpaolo Oriolo and Gautier Stauffer), we propose a new combinatorial algorithm for the maximum weighted stable set problem in claw-free graphs, and devise a robust algorithm for the same problem in the subclass of fuzzy circular interval graphs, which also provides recognition when the stability number is greater than three

show abstract

“…It also allows for building the mapping function in linear time. The overall complexity of the method compares favorably with the known results (see Muzychuk 2004).…”

Section: The Isomorphism and Coloring Problems On Circulant Graphssupporting

confidence: 70%

Some classical combinatorial problems on circulant and claw-free graphs: the isomorphism and coloring problems on circulant graphs and the stable set problem on claw-free graphs

Pietropaoli

2008

4OR-Q J Oper Res

View full text Add to dashboard Cite

show abstract

“…For n square free, we determine the normalizer of Aut(D S n ) (in Sym(n)) and use this result to formulate a general theorem concerning the automorphism group of End (D S n ). We use the latter theorem to determine the automorphism groups of End (D S n ) for some circulant digraphs D S n containing 2-cycles and the circulant digraphs D S n such that S = {0, s, t} where s and t are relatively prime to n. (It is worth observing that circulant digraphs attracted the attention of many mathematicians and other scientists leading to hundreds of papers written in the last few decades; see for example [2,10,[17][18][19]23].) Finally, in Section 5, we summarize the status of the problem of finding Aut(End (X, ρ)) given the results of this paper.…”

Section: Introductionmentioning

confidence: 99%

Automorphisms of endomorphism semigroups of reflexive digraphs

Araújo

Dobson

Konieczny

2010

Mathematische Nachrichten

View full text Add to dashboard Cite

A reflexive digraph is a pair (X, ρ), where X is an arbitrary set and ρ is a reflexive binary relation on X.Let End (X, ρ) be the semigroup of endomorphisms of (X, ρ). We determine the group of automorphisms of End (X, ρ) for: digraphs containing an edge not contained in a cycle, digraphs consisting of arbitrary unions of cycles such that cycles of length ≥ 2 are pairwise disjoint, and some circulant digraphs.

show abstract

“…, l n }. The L n i are based on circulant graphs-a class of graphs for which Muzychuk proved that the isomorphism problem can be solved in polynomial time (Muzychuk 2004).…”

Section: Labeled To Unlabeled Homeomorphismsmentioning

confidence: 99%

All normalized anti-monotonic overlap graph measures are bounded

Calders

Ramon

Dyck

2011

Data Min Knowl Disc

View full text Add to dashboard Cite

In graph mining, a frequency measure for graphs is anti-monotonic if the frequency of a pattern never exceeds the frequency of a subpattern. The efficiency and correctness of most graph pattern miners relies critically on this property. We study the case where frequent subgraphs have to be found in one graph. Vanetik et al. (Data Min Knowl Disc 13(2):243-260, 2006) already gave sufficient and necessary conditions for anti-monotonicity of graph measures depending only on the edge-overlaps between the instances of the pattern in a labeled graph. We extend these results to homomorphisms, isomorphisms and homeomorphisms on both labeled and unlabeled, directed and undirected graphs, for vertex-and edge-overlap. We show a set of reductions between the different morphisms that preserve overlap. As a secondary contribution, we prove that the popular maximum independent set measure assigns the minimal possible normalized frequency and we introduce a new measure based on the minimum clique partition that assigns the maximum possible normalized frequency. In that way, we obtain that all normalized anti-monotonic overlap graph measures are bounded from above and below. We also introduce a new measure sandwiched between the former two based on the polynomial time computable Lovász θ -function.

show abstract

A solution of the isomorphism problem for circulant graphs

Cited by 93 publications

References 17 publications

Some classical combinatorial problems on circulant and claw-free graphs: the isomorphism and coloring problems on circulant graphs and the stable set problem on claw-free graphs

Some classical combinatorial problems on circulant and claw-free graphs: the isomorphism and coloring problems on circulant graphs and the stable set problem on claw-free graphs

Automorphisms of endomorphism semigroups of reflexive digraphs

All normalized anti-monotonic overlap graph measures are bounded

Contact Info

Product

Resources

About