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DISTINGUISHING CHROMATIC NUMBER OF THE HIERARCHICAL PRODUCT OF GRAPHS
Hacettepe Journal of Mathematics and StatisticsThe distinguishing chromatic number $\chi_D(G)$ of a graph $G$ is the smallest number of colors needed to properly color the vertices of $G$ such that the only automorphism of $G$ that preserves colors is the identity. Studying the distinguishing chromatic number of graphs produced some interesting work, and in continuation, we may prefer to ...
T. Amouzegar
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On the Vertex-Distinguishing Edge Chromatic Number of 𝐏𝐦 ∨ 𝐂𝐧
DEStech Transactions on Engineering and Technology Research, 2017 A proper edge coloring of graph G is called equitable adjacent strong edge coloring if colored sets from every two adjacent vertices incident edge are different, and the number of edges in any two color classes differ by at most one, which the required minimum number of colors is called the adjacent strong equitable edge chromatic number. In this paper,
Chuan-cheng ZHAO +2 more
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Upper bounds on adjacent vertex distinguishing total chromatic number of graphs
Discrete Applied Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaolan Hu, Yunqing Zhang, Zhengke Miao
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Distinguishing Chromatic Numbers of Bipartite Graphs [PDF]
The Electronic Journal of Combinatorics, 2009 Extending the work of K.L. Collins and A.N. Trenk, we characterize connected bipartite graphs with large distinguishing chromatic number. In particular, if $G$ is a connected bipartite graph with maximum degree $\Delta \geq 3$, then $\chi_D(G)\leq 2\Delta -2$ whenever $G\not\cong K_{\Delta-1,\Delta}$, $K_{\Delta,\Delta}$.
Laflamme, C., Seyffarth, K.
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Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree
Axioms, 2023 Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing ...
Jingjing Huo +3 more
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Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs
Mathematics, 2023 In this paper, we consider the adjacent vertex distinguishing proper edge coloring (for short, AVDPEC) and the adjacent vertex distinguishing total coloring (for short, AVDTC) of a fuzzy graph.
Zengtai Gong, Chen Zhang
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The Distinguishing Chromatic Number of the Graph, C_n ? I_m [PDF]
, 2020 Donny K. Tang
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Adjacent vertex distinguishing acyclic edge coloring of the Cartesian product of graphs [PDF]
Transactions on Combinatorics, 2017 Let $G$ be a graph and $chi^{prime}_{aa}(G)$ denotes the minimum number of colors required for an acyclic edge coloring of $G$ in which no two adjacent vertices are incident to edges colored with the same set of colors. We prove a general bound for $
Fatemeh Sadat Mousavi, Massomeh Noori
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The chromatic distinguishing index of certain graphs
AKCE International Journal of Graphs and Combinatorics, 2020 The distinguishing index of a graph , denoted by , is the least number of labels in an edge coloring of not preserved by any non-trivial automorphism. The distinguishing chromatic index of a graph is the least number such that has a proper edge coloring ...
Saeid Alikhani, Samaneh Soltani
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On Adjacent Vertex-distinguishing Equitable-total Chromatic Number of Pm ∨ Fm
, 2021 Suppose the simple graph G(V, E) is at least 2nd-order connected. We study the adjacent vertex-distinguishing equitable-total coloring of the join graph Pm ∨ Fm which belongs to the graph G(V, E). By constructing the total coloring of Pm ∨ Fm , we obtain
Jishun Wang +3 more
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