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1981•SIAM Journal on ComputingRequires access

Some NP-Complete Problems Similar to Graph Isomorphism

Anna Lubiw

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Abstract

The GRAPH ISOMORPHISM problem has so far resisted attempts at determining its complexity status—it has not been shown to be NP-complete nor in P. In this paper several altered or generalized versions of the ISOMORPHISM problem are presented and shown to be NP-complete. One of these is the problem of determining whether a given graph has a fixed-point-free automorphism. Some speculation is made on the possible implications of these results on deciding the complexity status of ISOMORPHISM. Various classes and hierarchies of problems in NP are discussed.

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What this paper is about

The GRAPH ISOMORPHISM problem has so far resisted attempts at determining its complexity status—it has not been shown to be NP-complete nor in P. In this paper several altered or generalized versions of the ISOMORPHISM problem are presented and shown to be NP-complete. One of these is the problem of determining whether a given graph has a fixed-point-free automorphism. Some speculation is made on the possible implications of these results on deciding the complexity status of ISOMORPHISM. Various classes and hierarchies of problems in NP are discussed.

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Available abstract

The GRAPH ISOMORPHISM problem has so far resisted attempts at determining its complexity status—it has not been shown to be NP-complete nor in P. In this paper several altered or generalized versions of the ISOMORPHISM problem are presented and shown to be NP-complete. One of these is the problem of determining whether a given graph has a fixed-point-free automorphism. Some speculation is made on the possible implications of these results on deciding the complexity status of ISOMORPHISM. Various classes and hierarchies of problems in NP are discussed.

Key concepts: Graph isomorphism, Graph automorphism, Induced subgraph isomorphism problem, Mathematics, Isomorphism (crystallography), Subgraph isomorphism problem, Combinatorics, Automorphism

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