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Permutation Graph


For a permutation alpha in the symmetric group S_p, the alpha-permutation graph of a labeled graph G is the graph union of two disjoint copies of G (say, G_1 and G_2), together with the lines joining point v_i of G_i with v_(alpha(i)) of G_2 (Harary 1994, p. 175).

PermutationGraph

Skiena (1990, p. 28) defines a permutation graph G_p as a graph whose edges {v_i,v_j} correspond exactly to (i,j) being a permutation inversion is some permutation p, i.e., i<j but j occurs before i in p. The above graph corresponds to the permutation {2,1,5,6,7,10,9,4,8,3}, which has permutation inversion {2,1,10,8,3,4,5,9,7,6}. Permutation graphs are implemented as PermutationGraph[p] in the Wolfram Language package Combinatorica` .


See also

Permutation, Permutation Group, Permutation Inversion

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References

Atallah, M. J.; Manacher, G. K.; and Urrutia, J. "Finding a Minimum Independent Dominating Set in a Permutation Graph." Discr. Appl. Math. 21, 177-183, 1988.Brandstadt, A. and Kratsch, D. "On Domination Problems for Permutation and Other Graphs." Theoret. Comput. Sci. 54, 181-198, 1987.Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.

Referenced on Wolfram|Alpha

Permutation Graph

Cite this as:

Weisstein, Eric W. "Permutation Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PermutationGraph.html

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