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The list distinguishing number of Kneser graphs [PDF]
Discrete Applied Mathematics, 2018 A graph $G$ is said to be $k$-distinguishable if the vertex set can be colored using $k$ colors such that no non-trivial automorphism fixes every color class, and the distinguishing number $D(G)$ is the least integer $k$ for which $G$ is $k$-distinguishable.
Niranjan Balachandran +1 more
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Distinguishing Numbers for Graphs and Groups [PDF]
The Electronic Journal of Combinatorics, 2004 A graph $G$ is distinguished if its vertices are labelled by a map $\phi: V(G) \longrightarrow \{1,2,\ldots, k\}$ so that no non-trivial graph automorphism preserves $\phi$. The distinguishing number of $G$ is the minimum number $k$ necessary for $\phi$ to distinguish the graph. It measures the symmetry of the graph.
Julianna Tymoczko, Tymoczko, Julianna
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Distinguishing graphs by the number of homomorphisms [PDF]
Discussiones Mathematicae Graph Theory, 1995 A homomorphism from one graph to another is a mapping that sends vertices to vertices and edges to edges. Let \(|G\to H|\) denote the number of homomorphisms from \(G\) to \(H\). For example \(|G\to K_n|\) is the number of \(n\)-colorings of \(G\). If \(\mathcal F\) is a collection of graphs, we say that \(\mathcal F\) distinguishes graphs \(G\) and ...
Fisk, Steve
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All Graphs of Order n with Distinguishing Number n−1 or n − 2 [PDF]
Theory and Applications of GraphsLet G be a simple connected graph. The distinguishing number of G, denoted by D(G), is the least integer d such that G has a vertex d-labeling preserved only by the trivial automorphism.
Andi Pujo Rahadi +2 more
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Distinguishing number and distinguishing index of some operations on graphs
Journal of Information and Optimization Sciences, 2018 11 pages, 4 ...
Saeid Alikhani, Samaneh Soltani
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THE COST NUMBER AND THE DETERMINING NUMBER OF A GRAPH [PDF]
Journal of Algebraic Systems, 2021 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 a trivial automorphism. The minimum size of a label class in such a labeling of $G$ with $D(G) = d$ is
S. Alikhani, S. Soltani
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Distinguishing index of Kronecker product of two graphs
Electronic Journal of Graph Theory and Applications, 2021 The distinguishing index D'(G) of a graph G is the least integer d such that G has an edge labeling with d labels that is preserved only by a trivial automorphism. The Kronecker product G x H of two graphs G and H is the graph with vertex set V(G) x V(H)
Saeid Alikhani, Samaneh Soltani
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The Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2006 In this paper we define and study the distinguishing chromatic number, $\chi_D(G)$, of a graph $G$, building on the work of Albertson and Collins who studied the distinguishing number. We find $\chi_D(G)$ for various families of graphs and characterize those graphs with $\chi_D(G)$ $ = |V(G)|$, and those trees with the maximum chromatic distingushing ...
Karen L. Collins, Ann N. Trenk
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Bounds on the Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2009 Collins and Trenk define the distinguishing chromatic number $\chi_D(G)$ of a graph $G$ to be the minimum number of colors needed to properly color the vertices of $G$ so that the only automorphism of $G$ that preserves colors is the identity. They prove results about $\chi_D(G)$ based on the underlying graph $G$.
Karen L. Collins +2 more
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Independent Exact Permutation Testing Algorithm for Distinguishing Sequential Pattern Discovery [PDF]
Jisuanji gongcheng, 2021 Traditional distinguishing sequential pattern mining algorithms usually generate a number of false positive patterns in their results, which hinder the subsequent decisions of tasks.
WU Jun, OUYANG Aijia, ZHANG Lin
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