r-Chromatic Number On r-Dynamic Vertex Coloring of Comb Graph
DOI:
https://doi.org/10.20956/j.v20i2.32143Keywords:
r-Dynamic coloring, chromatic number, comb graph, central graph, middle graphAbstract
Let be a graph with vertex set and edge set . An r-dynamic vertex coloring of a graph is a assigning colors to the vertices of such that for every vertex receives at least colors in its neighbors. The minimum color used in r-dynamic vertex coloring of graph is called the r-dynamic chromatic number denoted as . In this research we well determine the coloring pattern and the r-dynamic chromatic number of the comb graph , central graph of comb graph , middle graph of comb graph , line graph of comb graph , sub-division graf of comb graph , and para-line graph of comb graph Let be a graph with vertex set and edge set . An r-dynamic vertex coloring of a graph is a assigning colors to the vertices of such that for every vertex receives at least colors in its neighbors. The minimum color used in r-dynamic vertex coloring of graph is called the r-dynamic chromatic number denoted as . In this research we well determine the coloring pattern and the r-dynamic chromatic number of the comb graph , central graph of comb graph , middle graph of comb graph , line graph of comb graph , sub-division graf of comb graph , and para-line graph of comb graph
References
Alishahi, M., 2012. Dynamic Chromatic Number of Regular Graphs.
Discrete Applied Mathematics, 160, 2098–2103.
Alfian, Y. H., Ika. H. A., and Dafik, 2015. Pewarnaan Titik Pada Operasi
Graf Sikel dengan Graf Lintasan. CGANT Universitas Jember
Audi Fierera and Kiki A. Sugeng, 2021. Pewarnaan Simpul r-Dinamis pada
Graf Teratai T_n. Ambon, Universitas Pattimura
Chartrand, G., dan. Zhang.P., 2009. Chromatic Graph Theory of a Graph.
USA: CRC Press
Frucht, R., dan Harary, F., 1970. On The Corona of Two Graphs. Vol. 4, Santa Maria University dan University of Michigan
Harary, F., 1969. Graph Theory, Narosa Publishing Home, New Delhi.
Hasmawati. 2020. Pengantar dan Jenis-Jenis Graf. UPT Unhas Press
Kalaiselvi, K., Mohanapriya, and Vernold, V.J., 2021. On r-Dynamic
Coloring of Comb Graph. Vol. 27, 2021, No. 2, 191–200
Lai, H. J., and Montgomery, B., 2001. Dynamic Coloring of Graphs. West
Virginia University, Morgantown
Lai, H. J., Montgomery, B., Poon, H., 2003. Upper Bounds of Dynamic
Chromatic Number. Ars Combinatoria 68
Michalak, D., 1983. On Middle and Total Graphs with Coarseness
Number Equal 1. Lecture Notes in Mathematics, 1018, Springer Verlag
Graph Theory, Lagow proceedings, Berlin Heidelberg, New York, Tokyo,
–150.
Muhammad,D.T., 2015. Nilai Kromatik dan Pewarnaan Titik r
Dinamis pada Graf Khusus dan Shakel. Jember: Universitas Jember
Novian N.F., 2015. Pewarnaan Titik dan Sisi r-Dinamis Pada Graf
Hasil Operasi Comb Sisi. Jombang.
Slamin, 2009. Desain Jaringan Pendekatan Teori Graf. Jember: Universitas
Jember.
Taherkhani, A., 2016. r-Dynamic Chromatic Number of Graphs. Discrete
Applied Mathematics, 201, 222-227
Vernold V. J., 2007. Harmonious Coloring of Total Graphs, n-leaf,
Central Graphs and Circumdetic Graphs, Ph.D. Thesis, Bharathiar
University, Coimbatore, India.
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