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Journal of Mathematical Chemistry

, Volume 56, Issue 5, pp 1437–1444 | Cite as

Computing the maximal canonical form for trees in polynomial time

  • Gunnar Brinkmann
Original Paper
  • 39 Downloads

Abstract

Known algorithms computing a canonical form for trees in linear time use specialized canonical forms for trees and no canonical forms defined for all graphs. For a graph \(G=(V,E)\) the maximal canonical form is obtained by relabelling the vertices with \(1,\ldots ,|V|\) in a way that the binary number with \(|V|^2\) bits that is the result of concatenating the rows of the adjacency matrix is maximal. This maximal canonical form is not only defined for all graphs but even plays a special role among the canonical forms for graphs due to some nesting properties allowing orderly algorithms. We give an \(O(|V|^2)\) algorithm to compute the maximal canonical form of a tree.

Keywords

Tree Canonical form Structure enumeration 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Applied Mathematics, Computer Science and StatisticsGhent UniversityGhentBelgium

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