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The R-Dynamic Local Irregularity Vertex Coloring Of Graph
[Full Text]
AUTHOR(S)
A. I. Kristiana, M. I. Utoyo, Dafik, R. Alfarisi, E. Waluyo
KEYWORDS
r-dynamic coloring, local irregularity, vertex coloring.
ABSTRACT
We define the r-dynamic local irregularity vertex coloring. Suppose : V(G) {1,2, … , k} is called vertex irregular k-labeling and w : V(G) N where w(u)=∑_(v∈N(u))▒〖(v)〗. is called r-dynamic local irregular vertex coloring, if: (i) opt() = min{max{i}; i vertex irregular k-labeling}, (ii) for every uv E(G), w(u) ≠ w(v), and (iii) for every v V(G) such that |w(N(v))| min{r, d(v)}. The chromatic number r-dynamic local irregular denoted by χ_lis^r (G), is minimum of cardinality r-dynamic local irregular vertex coloring. We study the r-dynamic local irregularity vertex coloring of graph and we have found the exact value of chromatic number r-dynamic local irregularity of some graph.
REFERENCES
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[4] A. I. Kristiana, M. I. Utoyo, Dafik, R. Alfarisi, I. H. Agustin, and E. Waluyo., ” On the chromatic number local irregularity of related wheel graph,” Journal of Physics: Conf. Series, 1211, 012003, 2019.
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