Results 11 to 20 of about 5,516,987 (160)
List distinguishing index of graphs [PDF]
Ars Mathematica Contemporanea, 2023 We say that an edge colouring breaks an automorphism if some edge is mapped to an edge of a different colour. We say that the colouring is distinguishing if it breaks every non-identity automorphism. We show that such colouring can be chosen from any set
Jakub Kwa'sny, Marcin Stawiski
semanticscholar +3 more sources
European Journal of Combinatorics, 2020 The distinguishing number of a group A acting on a finite set Ω , denoted by D ( A , Ω ) , is the least k such that there is a k -coloring of Ω which is preserved only by elements of A fixing all points in Ω .
M. Pilsniak, T. Tucker
semanticscholar +3 more sources
A note on the neighbour-distinguishing index of digraphs [PDF]
Ars Mathematica Contemporanea, 2019 In this note, we introduce and study a new version of neighbour-distinguishing arc-colourings of digraphs. An arc-colouring $\gamma$ of a digraph $D$ is proper if no two arcs with the same head or with the same tail are assigned the same colour. For each
É. Sopena, M. Woźniak
semanticscholar +6 more sources
A bound for the distinguishing index of regular graphs [PDF]
European Journal of Combinatorics, 2019 An edge-colouring of a graph is distinguishing if the only automorphism that preserves the colouring is the identity. It has been conjectured that all but finitely many connected, finite, regular graphs admit a distinguishing edge-colouring with two ...
Florian Lehner +2 more
semanticscholar +5 more sources
Distinguishing Number and Distinguishing Index of the Join of Two Graphs [PDF]
Mathematics Interdisciplinary Research, 2019 The distinguishing number (index) D(G) (D'(G)) of a graph G is the least integer d such that G has an vertex labeling (edge labeling) with d labels that is preserved only by a trivial automorphism. In this paper we study the distinguishing number and the
Saeid Alikhani, Samaneh Soltani
doaj +2 more sources
Improving upper bounds for the distinguishing index
Ars Mathematica Contemporanea, 2017 The distinguishing index of a graph G , denoted by D ʹ( G ) , is the least number of colours in an edge colouring of G not preserved by any non-trivial automorphism. We characterize all connected graphs G with D ʹ( G ) ≥ Δ ( G ) . We show that D ʹ( G ) ≤
M. Pilsniak
semanticscholar +5 more sources
The Distinguishing Index of Infinite Graphs [PDF]
The Electronic Journal of Combinatorics, 2015 The distinguishing index $D^\prime(G)$ of a graph $G$ is the least cardinal $d$ such that $G$ has an edge colouring with $d$ colours that is only preserved by the trivial automorphism. This is similar to the notion of the distinguishing number $D(G)$ of
I. Broere, M. Pilsniak
semanticscholar +3 more sources
Distinguishing number and distinguishing index of certain graphs [PDF]
Filomat, 2016 The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$ labels that is preserved only by a trivial automorphism.
S. Alikhani, S. Soltani
semanticscholar +5 more sources
A Characterization for the Neighbor-Distinguishing Index of Planar Graphs
Symmetry, 2022 Symmetry, such as structural symmetry, color symmetry and so on, plays an important role in graph coloring. In this paper, we use structural symmetry and color symmetry to study the characterization for the neighbor-distinguishing index of planar graphs.
Jingjing Huo, Mingchao Li, Y. Wang
semanticscholar +2 more sources
Nordhaus-Gaddum type inequalities for the distinguishing index
Ars Mathematica Contemporanea, 2021 The distinguishing index of a graph G, denoted by D′(G), is the least number of colours in an edge colouring of G not preserved by any nontrivial automorphism.
M. Pilsniak
semanticscholar +3 more sources