On r-dynamic chromatic number of coronation of order two of any graphs with path graph

1st International Conference on Environmental Geography and Geography Education

生态环境科学;地球科学

Septory, B.J.^1^2 ; Dafik^1^2 ; Kristiana, A.I.^1^2 ; Agustin, I.H.^1^3 ; Wardani, D.A.R.^1^4

CGANT University of Jember, Indonesia^1

Mathematics Edu. Depart, University of Jember, Indonesia^2

Mathematics Depart, University of Jember, Indonesia^3

Mathematics Edu. Depart, IKIP PGRI Jember, Indonesia^4

关键词: Complete graphs;    Dynamic chromatic numbers;    Isolated vertices;    Lower bounds;    Path graphs;    Star graphs;    Two-graphs;    Undirected graph;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/243/1/012113/pdf
DOI  :  10.1088/1755-1315/243/1/012113

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

In this study we assume every graphs be a simple, finite, nontrivial, connected and undirected graphs with vertex set V(H), edge set E(H) and no isolated vertex. An r-dynamic coloring of a graph H is a proper k-coloring of graph H such that the neighbors of any vertex u accept at least min{r, d(u)} different colors. The r-dynamic chromatic number is the minimum k such that graph H has an r-dynamic k-coloring, it is shown by χr (H). In this research, we interpret the r-dynamic chromatic number of graph corona of order two, denoted by H 1o2 H 2. The corona of two graphs H 1 and H 2 is a graph H 1 o H 2 formed from one copy of H 1 and |V(H 1)| copies of H 2 where the ith vertex of H 1 is adjacent to every vertex in the ith copy of H 2. For any integer l ≥ 2, we establish the graph H 1 ol H 2 recursively from H 1 o H 2 as H 1 ol H 2 = (H 1 ol-1 H 2) o H 2. Graph H 1 ol H 2 is also named as l - corona product of H 1 and H 2. Xr = (Pn o2 H 2) and H 2 is path graph Pm , star graph Sm , complete graph Km and fan graph Fm . In this study we will determine the lower bound of r-dynamic chromatic number of corona order two of graphs.