Local antimagic vertex dynamic coloring of some graphs family

1st International Conference on Environmental Geography and Geography Education

生态环境科学;地球科学

Wardani, P.L.^1^2 ; Dafik^1^2 ; Kristiana, A.I.^1^2 ; Agustin, I.H.^1^3 ; Alfarisi, R.^1^4

CGANT-Research Group, University of Jember, Indonesia^1

Department of Mathematics Education, University of Jember, Indonesia^2

Department of Mathematics, University of Jember, Indonesia^3

Department of Elementary School Teacher Education, University of Jember, Indonesia^4

关键词: Antimagic;    Bijections;    Connected graph;    Dynamic chromatic numbers;    Dynamic graph;    Graph class;    K-coloring;    Neighbourhood;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/243/1/012115/pdf
DOI  :  10.1088/1755-1315/243/1/012115

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

All graphs in this paper are simple and connected graph. A vertex dynamic coloring is a proper vertex k-coloring of graph G such that |c(N(vi ))| ≥ min{r, d(v)} and the neighbourhood of vertex u has different colors. A bijection f : E(G) → {1, 2, 3, , m} is called a local antimagic dynamic coloring, such that: (1) if uv E(G), where w(u) = ∑eE(u) f(e) and (2) for each vertex v V(G), |w(N(vi ))| ≥ min{r, d(vi )}. The local antimagic vertex dynamic chromatic number denoted by is the minimum number of colors needed to color G in such a way the graph G to be local antimagic vertex dynamic graph. In this paper, we will study the existence of the local antimagic vertex dynamic chromatic number of some graph classes, namely caterpilar, doublebroom, broom and sun graph.