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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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Trees with Distinguishing Index Equal Distinguishing Number Plus One
Discussiones Mathematicae Graph Theory, 2020 The distinguishing number (index) D(G) (D′ (G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism.
Alikhani Saeid +3 more
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The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs
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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A New Game Invariant of Graphs: the Game Distinguishing Number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 The distinguishing number of a graph $G$ is a symmetry related graph invariant whose study started two decades ago. The distinguishing number $D(G)$ is the least integer $d$ such that $G$ has a $d$-distinguishing coloring.
Sylvain Gravier +3 more
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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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پژوهشهای ریاضی, 2020 Introduction The graph is a mathematical model for a discrete set whose members are interlinked in some way. The members of this collection can be the different parts of the earth and the connections between them are bridges that tie them together (like ...
Saeid Alikhani, Samaneh Soltani
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Distinguishing chromatic number of random Cayley graphs
Discrete Mathematics, 2017 11 ...
Niranjan Balachandran +1 more
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The Distinguishing Number and Distinguishing Index of the Lexicographic Product of Two Graphs
Discussiones Mathematicae Graph Theory, 2018 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 that is preserved only by the trivial automorphism.
Alikhani Saeid, Soltani Samaneh
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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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The Distinguishing Number and Distinguishing Chromatic Number for Posets [PDF]
Order, 2021 23 pages, 4 ...
Karen L. Collins, Ann N. Trenk
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