G). For proper distinguishing arc-colourings, the least number of colours is called the
distinguishing chromatic index of←→ G. There are 15 possible types of proper arc …

We consider edge colourings, not necessarily proper. The distinguishing index D (G) of a
graph G is the least number of colours in an edge colouring that is preserved only by the …

An edge-coloring of a graph is called asymmetric if the only automorphism which preserves
it is the identity. Lehner, Pilśniak, and Stawiski proved that all connected, locally finite …

The distinguishing index D′(G) D^′(G) of a graph GG is the least number of colors
necessary to obtain an edge coloring of GG that is preserved only by the trivial …

The distinguishing index D′(Γ) of a graph Γ is the least number k such that Γ has an edge-
coloring with k colors preserved only by the trivial automorphism. In this paper we prove that …

arXiv:2207.14728v2 [math.CO] 4 May 2023 Distinguishing regular graphs Page 1 arXiv:2207.14728v2
[math.CO] 4 May 2023 Distinguishing regular graphs Jakub Kwasny, Marcin Stawiski∗ AGH …

A graph automorphism is a bijective mapping of the vertices that preserves adjacent
vertices. A vertex determining set of a graph is a set of vertices such that the only …

The distinguishing number (index) D (G)(D^ ′ (G)) of a graph G is the least integer d such
that G has a vertex labeling (edge labeling) with d labels which is preserved only by a trivial …

A graph automorphism is a bijective mapping of the vertices that preserves adjacent
vertices. A vertex-determining set of a graph is a set of vertices such that the only …

Abstract As noted by Mariusz Grech and Andrzej Kisielewicz [1], the inequality on page 6,
line 9 of [2] is only valid if [Formula presented]. Hence the case [Formula presented]. This …