Open AccessOn the study of local antimagic vertex coloring of graphs and their operations
Author(s) -
Dafik Dafik,
Ika Hesti Agustin,
. Slamin,
Robiatul Adawiyah,
Elsa Yuli Kurniawati
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1836/1/012018
Subject(s) - combinatorics , bijection , mathematics , vertex (graph theory) , edge coloring , graph , chromatic scale , discrete mathematics , graph power , line graph
Arumugam paper studied in et al [4] has inspired us to study the same thing, namely local antimagic edge labeling of graphs. In this paper, we continue to study this type of coloring of some graphs and its operations. By a local antimagic edge labeling, we mean a bijection f from the edge set of G to the natural number up to the number of edges in G such that for any two adjacent vertices v and v’ have different weight, w(v) = w(v’), where w(v) = Σ e∈E(v) f ( e ), and E(v) is the set of vertices which is incident to v. Furthermore, the vertex weight w(v) is assigned as the color on a vertex of G. The local antimagic chromatic number χ 1α (G) is the minimum number of colors taken over all coloring induced by vertex local antimagic edge labeling of G .