1st International Conference on Environmental Geography and Geography Education | |
Local antimagic r-dynamic coloring of graphs | |
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 |
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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.
【 预 览 】
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Local antimagic r-dynamic coloring of graphs | 615KB | download |