On edge chromatic number related to local antimagic labeling of some trees

1st International Conference on Environmental Geography and Geography Education

生态环境科学;地球科学

Agustin, I.H.^1^2 ; Dafik^1^3 ; Alfarisi, R.^1^5 ; Kurniawati, E.Y.^1^2 ; Marsidi^1^4

CGANT-University of Jember, Jember, Indonesia^1

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

Department of Mathematics Education, University of Jember, Jember, Indonesia^3

Department Mathematics Edu., Indonesia^4

Department of Elementary School Education, University of Jember, Jember, Indonesia^5

关键词: Antimagic labeling;    Bijections;    Double stars;    Edge chromatic number;    Edge coloring;    Edge labeling;    Lower bounds;    Tree graph;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/243/1/012078/pdf
DOI  :  10.1088/1755-1315/243/1/012078

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

Tree graph is one of the simplest the most important classes of graphs. A tree is a graph having no cycles. Graph H(V, E) consists of a finite nonempty set V called vertices and element of E is called edge. Edge coloring is an assignment of labels color to edges of graph subject to certain constrains. Local antimagic total edge labeling is defined a bijection g : V (H) ∪ E(H) → {1,2, 3, , p + q}, where p and q are the number of vertices and edges, respectively. If for any two adjacent edges e 1 and e 2, wt (e 1) ≠ wt (e 2), where for e = xy ∈ H, wt (e) = g(x) + g(xy) + g(y). The local antimagic total edge labeling induces a proper edge coloring of H if each edge e is assigned the color wt (e). The local antimagic total edge chromatic number of H denoted by χlate (H), is the minimum of colors needed to color the edges of graph H. In this paper we determine the local antimagic total edge chromatic number of some families of trees, namely double star, broom, firecracker, and centipede graph. The all results attain the lower bound.