Local antimagic r-dynamic coloring of graphs

1st International Conference on Environmental Geography and Geography Education

生态环境科学;地球科学

Kristiana, A.I.^1^2^3 ; Utoyo, M.I.^3 ; Dafik^1^2 ; Agustin, I.H.^1^2 ; Alfarisi, R.^1

CGANT-University of Jember, Jember, Indonesia^1

University of Jember, Jember, Indonesia^2

University of Airlangga, Surabaya, Indonesia^3

关键词: Antimagic;    Antimagic labeling;    Basic results;    Bijections;    Connected graph;    Dynamic chromatic numbers;    K-coloring;    Upper Bound;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/243/1/012077/pdf
DOI  :  10.1088/1755-1315/243/1/012077

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

Let G = (V, E) be a connected graph. A bijection function f : E(G) → {1,2, 3, • • •, E(G)|} is called a local antimagic labeling if for all uv ∈ E(G)s, w(u) ≠ w(v), where w(u) = ∑e∈E(u) f(e). Such that, local antimagic labeling induces a proper vertex k-coloring of graph G that the neighbors of any vertex u receive at least min{r, d(v)} different colors. The local antimagic r-dynamic chromatic number, denoted by (G) is the minimum k such that graph G has the local antimagic r-dynamic vertex k-coloring. In this paper, we will present the basic results namely the upper bound of the local antimagic r-dynamic chromatic number of some classes graph.