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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Katanaga, Atsuko
Iwate University
Electrical & Electronics Engineering

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Graph-theoretic properties of inversion-transpositions Katanaga, Atsuko; Shiratama, Takahiro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 1 (2026): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2026.14.1.6

Abstract

Dénés established the connection between labeled trees in Graph Theory and factorizations of cyclic permutations by means of transpositions. In this paper, we introduce the notion of an inversion-transposition, which has both the properties of an inversion and a transposition. For a cyclic permutation, we define the graph associated with each minimal representation using only inversion-transpositions and consider the properties. The main result is that a spanning tree T reconstructs the original permutation if and only if the sum over all vertices v of the distance in T between v and σ(v) equals 2(n - 1), which provides a precise reconstruction criterion.
Co-Authors Shiratama, Takahiro