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The Adjacent Vertex Distinguishing Total Chromatic Number of Graphs

2010 4th International Conference on Bioinformatics and Biomedical Engineering, 2010
Let $G=(V,E)$ be a graph and $f$:$(V\cup E)\rightarrow [k]$ be a proper total $k$-coloring of $G$.We say that $f$ is an adjacent vertex distinguishing total coloring if for any two adjacent vertices,the set of colors appearing on the vertex and incident edges are different.We call the smallest $k$ for which such a coloring of $G$ exists the adjacent ...
Zhiwen Wang, Enqiang Zhu
openaire   +1 more source

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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Relations of vertex distinguishing total chromatic numbers between a subgraph and its supergraph

Information Sciences, 2014
Xiang’En Chen
exaly  

Chromatic number is Ramsey distinguishing

Journal of Graph Theory, 2022
exaly  

On the Adjacent Vertex Strong Distinguishing Total Chromatic Number of Some Graphs

2013
exaly  

On the adjacent vertex distinguishing edge chromatic number of graphs.

Ars Comb., 2016
openaire  

The adjacent vertex-distinguishing total chromatic number of 1-tree.

Ars Comb., 2009
openaire