Results 1 to 10 of about 16,459 (227)
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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On the distinguishing chromatic number of the Kronecker products of graphs
AKCE International Journal of Graphs and Combinatorics, 2023 In this paper, we investigate the distinguishing chromatic number of Kronecker product of paths, cycles, star graphs, symmetric trees, almost symmetric trees, and bisymmetric trees.
Zinat Rastgar +2 more
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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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Distinguishing Chromatic Number of Random Cayley graphs
Discrete Mathematics, 2016 The \textit{Distinguishing Chromatic Number} of a graph $G$, denoted $\chi_D(G)$, was first defined in \cite{collins} as the minimum number of colors needed to properly color $G$ such that no non-trivial automorphism $\phi$ of the graph $G$ fixes each ...
Balachandran, Niranjan +1 more
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Equitable distinguishing chromatic number
Indian Journal of Pure and Applied Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tayyebeh Amouzegar, Kazem Khashyarmanesh
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Neighbor Sum Distinguishing Total Chromatic Number of Planar Graphs without 5-Cycles
Discussiones Mathematicae Graph Theory, 2020 For a given graph G = (V (G), E(G)), a proper total coloring ϕ: V (G) ∪ E(G) → {1, 2, . . . , k} is neighbor sum distinguishing if f(u) ≠ f(v) for each edge uv ∈ E(G), where f(v) = Σuv∈E(G) ϕ(uv)+ϕ(v), v ∈ V (G). The smallest integer k in such a coloring
Zhao Xue, Xu Chang-Qing
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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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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 ...
Collins, Karen L., Trenk, Ann N.
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AVD proper edge-coloring of some families of graphs
International Journal of Mathematics for Industry, 2021 Adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for the proper edge-coloring of [Formula: see text] in which no two adjacent vertices are incident to edges colored with the same set of colors.
J. Naveen
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Chromatic number is Ramsey distinguishing [PDF]
Journal of Graph Theory, 2021 AbstractA graph is Ramsey for a graph if every colouring of the edges of in two colours contains a monochromatic copy of . Two graphs and are Ramsey equivalent if any graph is Ramsey for if and only if it is Ramsey for . A graph parameter is Ramsey distinguishing if implies that and are not Ramsey equivalent.
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