The chromatic number of local antimagic total edge coloring of some related cycle graphs

1st International Conference on Environmental Geography and Geography Education

生态环境科学;地球科学

Kurniawati, E.Y.^1^2 ; Dafik^1^3 ; Agustin, I.H.^1^2 ; Prihandini, R.M.^1^4 ; Nisviasari, R.^1^2

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

关键词: Bijections;    Chromatic number;    Cycle graphs;    Edge chromatic number;    Edge coloring;    Edge labeling;    Edge labels;    Undirected graph;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/243/1/012118/pdf
DOI  :  10.1088/1755-1315/243/1/012118

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

A graph G = (V, E) be connected, finite, and undirected graph without multiple edges and loops. Graph G(V, E) consists two sets of vertices V and edge E. A graph called related cycle if the subgraph of graph G contains a cycle. Local antimagic total edge labeling is defined a bijection f : V ∪ E → {1, 2, 3, , |V | + |E|}, if for any two adjacent edges e 1 and e 2, wt (e 1) ≠ wt (e 2), where for e = ab ∈ G, wt (e) = f(a) + f(ab) + f(b). Thus, the local antimagic total edge labeling induces a proper edge coloring of G if each edge e is assigned the color wt (e). The local antimagic total edge chromatic number of G denoted by γ late (G), is the minimum of colors needed to coloring the edges of a graph, the number of distinct induced edge labels over all local antimagic total labeling of G. In this paper we study the local antimagic total edge coloring of some related cycle of graphs and determined the chromatic number of some related cycle graphs namely triangular book Btr , prism graph Pr , sun graph Mr and kite graph Kr, s .