an:06880787
Zbl 1388.05035
Brinkmann, Gunnar
Computing the maximal canonical form for trees in polynomial time
EN
J. Math. Chem. 56, No. 5, 1437-1444 (2018).
00388636
2018
j
05C05 05C85 05C90 92E10
canonical form; structure enumeration
Summary: 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 \(1,\dots,|V|\) 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.