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The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2017 A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring
Immel Poppy, Wenger Paul S.
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On the Distinguishing Number of Functigraphs [PDF]
Symmetry, 2018 Let G 1 and G 2 be disjoint copies of a graph G and g : V ( G 1 ) → V ( G 2 ) be a function. A functigraph F G consists of the vertex set V ( G 1 ) ∪ V ( G 2 ) and the edge set E ( G 1 ) ∪ E ( G 2 ) ∪ { u v : g ( u ) = v } .
Usman Ali +2 more
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The distinguishing number of the hypercube [PDF]
Discrete Mathematics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lenore Cowen
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The distinguishing number and the distinguishing index of line and graphoidal graph(s)
AKCE International Journal of Graphs and Combinatorics, 2020 The distinguishing number (index) () of a graph is the least integer such that has a vertex labeling (edge labeling) with labels that is preserved only by a trivial automorphism.
Saeid Alikhani, Samaneh Soltani
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On the graphs with distinguishing number equal list distinguishing number [PDF]
Journal of Mahani Mathematical Research, 2023 The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling with $d$ labels that is preserved only by the trivial automorphism.
Saeid Alikhani, Samaneh Soltani
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On the local distinguishing chromatic number [PDF]
AKCE International Journal of Graphs and Combinatorics, 2019 The distinguishing number of graphs is generalized in two directions by Cheng and Cowen (local distinguishing number) and Collins and Trenk (Distinguishing chromatic number). In this paper, we define and study the local distinguishing chromatic number of
Omid Khormali
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The Distinguishing Number and Distinguishing Chromatic Number for Posets [PDF]
Order, 2021 23 pages, 4 ...
Ann Trenk, Karen L Collins, Trenk Ann N
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Trees with distinguishing number two [PDF]
AKCE International Journal of Graphs and Combinatorics, 2019 The distinguishing number of a graph is the least integer such that has a vertex labeling with labels that is preserved only by a trivial automorphism. In this paper we characterize all trees with radius at most three and distinguishing number two.
Saeid Alikhani, Samaneh Soltani
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Number of distinguishing colorings and partitions [PDF]
Discrete Mathematics, 2020 A vertex coloring of a graph $G$ is called distinguishing (or symmetry breaking) if no non-identity automorphism of $G$ preserves it, and the distinguishing number, shown by $D(G)$, is the smallest number of colors required for such a coloring. This paper is about counting non-equivalent distinguishing colorings of graphs with $k$ colors.
Mohammad Hadi Shekarriz, Bahman Ahmadi
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The Distinguishing Numbers and the Distinguishing Indexes of Cayley Graphs
Journal of Applied and Industrial Mathematics, 2021 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 investigate the distinguishing number and the distinguishing index of Cayley graphs.
Saeid Alikhani
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