isomorphism problem

isomorphism problem

[‚ī·sə′mȯr‚fiz·əm ‚präb·ləm]
(mathematics)
For two simple graphs with the same numbers of vertices and edges, the problem of determining whether there exist correspondences between these vertices and edges such that there is an edge between two vertices in one graph if and only if there is an edge between the corresponding vertices in the other.
References in periodicals archive ?
Among the topics are Lie algebras of special derivation, the isomorphism problem, and pairings of induced modules.
A new algorithm efficiently solves the graph isomorphism problem, computer scientist Laszlo Babai announced November 10 at a Combinatorics and Theoretical Computer Science seminar at the University of Chicago.
The graph isomorphism problem requires a computer to examine two graphs that may look very different and determine whether all the balls share the same connections.
Combinatorial Methods for the Graph Isomorphism Problem
Budapest): On the Isomorphism Problem of Cayley Graphs
9 DNA COMPUTING FOR SUBGRAPH ISOMORPHISM PROBLEM AND RELATED PROBLEMS (Sun-Yuan Hsieh, Chao-Wen Huang, and Hsin-Hung Chou).
Among their topics are the isomorphism problem for Coxeter groups, hyperbolic Coxeter groups and space forms, equivelar polyhedra, configurations of points and lines, and the reciprocal inspiration of Coxeter and artists.
Examples include simultaneous surface resolution in quadratic and biquadratic Galois extensions, asymptotic behavior of cohomology, conic divisor classes over a normal monoid algebra, Rees algebras of the second syzygy module of the residue field of a regular local ring, a local global principle for the elementary unimodular vector group, picture invariants and the isomorphism problem for complex semisimple Lie algebras, arithmetic rank of certain Segre products, and strong semistability and Hilbert-Kunz multiplicity for singular plane curves.
Some such problems of practical relevance include fundamental partition problems in graph theory, isomorphism problems in combinatorics, and strategy-design problems in mathematical game theory.