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The distinguishing chromatic numbers of triangulations on the sphere

The distinguishing chromatic numbers of triangulations on the sphere
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Distinguishing Chromatic Number of Cartesian Products of Graphs

SIAM Journal on Discrete Mathematics, 2010
The distinguishing chromatic number $\chi_{_D}(G)$ of a graph $G$ is the least integer $k$ such that there is a proper $k$-coloring of $G$ which is not preserved by any nontrivial automorphism of $G$. We study the distinguishing chromatic number of Cartesian products of graphs by focusing on how much it can exceed the trivial lower bound of the ...
Jeong Ok Choi, Stephen G. Hartke, Hemanshu Kaul   +2 more
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Neighbor sum distinguishing total chromatic number of 2-degenerate graphs

Discrete Applied Mathematics, 2018
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Xu, Changqing, Ge, Shan, Li, Jianguo
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Neighbor sum distinguishing total chromatic number of planar graphs

Applied Mathematics and Computation, 2018
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Xu, Changqing, Li, Jianguo, Ge, Shan
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A note on the line‐distinguishing chromatic number and the chromatic index of a graph

Journal of Graph Theory, 1993
AbstractLet λ(G) be the line‐distinguishing chromatic number and x′(G) the chromatic index of a graph G.We prove the relation λ(G) ≥ x′(G), conjectured by Harary and Plantholt. © 1993 John Wiley & Sons, Inc.
N. Z. Salvi
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The Edge-Distinguishing Chromatic Number of Paths and Cycles

1988
The edge-distinguishing chromatic number x 1 (G) of a graph G is defined as the minimum number n of colors { 1,2,…,n} which can be assigned to the vertices V(G) in such a way that when each edge e = uv is assigned as its “color” the set of colors {c(u), c (v)}, all the edges of G have different colors.
K. Al-Wahabi, R. Bari, F. Harary, D. Ullman   +3 more
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Neighbor sum distinguishing total chromatic number of K 4-minor free graph

Frontiers of Mathematics in China, 2017
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Song, Hongjie, Xu, Changqing
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On Adjacent Vertex-Distinguishing Total Chromatic Number of Generalized Petersen Graphs

2016 IEEE First International Conference on Data Science in Cyberspace (DSC), 2016
Analyzing chromatic number in coloring problem is a tough topic in graph analysis. We focus on the basic theory for a particular type of chromatic number. This will give us insights on the basic topological structure guiding lots of networks in the coming trend of big data era.
Enqiang Zhu, Fei Jiang, Zepeng Li, Zehui Shao, Jin Xu   +4 more
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Distinguishing chromatic numbers of complements of Cartesian products of complete graphs

Discrete Mathematics, 2018
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Cavers, M. S., Seyffarth, K., White, E. P.   +2 more
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Vertex Distinguishing Equitable Total Chromatic Number of Join Graph

Acta Mathematicae Applicatae Sinica, English Series, 2007
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Wang, Zhi-Wen, Yan, Li-Hong, Zhang, Zhong-Fu   +2 more
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