Graph isomorphism is in the low hierarchy
Journal of Computer and System Sciences
Subgraph isomorphism for biconnected outerplanar graphs in cubic time
Theoretical Computer Science
Geometric symmetry in graphs
Fast detection and display of symmetry in outerplanar graphs
Discrete Applied Mathematics
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
SCG '85 Proceedings of the first annual symposium on Computational geometry
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
How to Draw a Planar Clustered Graph
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
Validating Graph Drawing Aesthetics
GD '95 Proceedings of the Symposium on Graph Drawing
Which Aesthetic has the Greatest Effect on Human Understanding?
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Planarity for Clustered Graphs
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Designing Graph Drawings by Layout Graph Grammars
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Linear pattern matching algorithms
SWAT '73 Proceedings of the 14th Annual Symposium on Switching and Automata Theory (swat 1973)
On Maximum Symmetric Subgraphs
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Computing and Drawing Isomorphic Subgraphs
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Automatic classification of semantic user interface services
Ontology-Driven Software Engineering
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We are interested in finding symmetries in graphs and then use these symmetries for graph drawing algorithms. There are two general approaches to this problem, the first one is known as GEOMETRIC SYMMETRICS on the basis of drawings, the other rests upon the graph-theoretical notion of graphs. For a given graph G the ISOMORPHIC SUBGRAPHS problem makes use of the second approach and tries to find the two largest disjoint isomorphic subgraphs in G. Hence, G consists of two identical copies and a remainder. There are many NP-complete or open problems related to our problem, like GRAPH ISOMERPHISM, GRAPH AUTOMORPHISM or Largest LARGEST COMMON SUBGRAPH. We show that the ISOMORPHIC SUBGRAPHS problem is NP-hard for connected outerplanar graphs, and 2-connected planar graphs and is solvable in linear time when restricted to trees. Additionally we will shortly discuss the applicability of ISOMORPHIC SUBGRAPHS in graph drawing algorithms.