On the local super antimagic total face chromatic number of plane graphs

1st International Conference on Environmental Geography and Geography Education

生态环境科学;地球科学

Anggraini, D.D.^1^3 ; Dafik^1^3 ; Maryati, T.K.^2 ; Agustin, I.H.^1^4 ; Kurniawati, E.Y.^1^4 ; Prihandini, R.M.^1^5

CGANT-University of Jember, Jember, Indonesia^1

Department of Mathematics Education, State Islamic University (UIN) Syarif Hidayatullah, Jakarta, Indonesia^2

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

Department of Mathematics, University of Jember, Jember, Indonesia^4

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

关键词: Chromatic number;    Chromatic number of graphs;    Edge coloring;    Friendship graphs;    Ladder graphs;    Plane graphs;    Total chromatic number;    Vertex labeling;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/243/1/012015/pdf
DOI  :  10.1088/1755-1315/243/1/012015

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

Local antimagic total face labeling is a bijection f: V(G) ∪ E(G) ∪ F(G) → {1,2, 3, , |V(G)| + |E(G)| + |F(G)|} and for every two adjacent F 1 and F 2, wt (F 1) ≠ wt (F 2), where F ∈ G, wt (F) = ∑vV(A) f(v) + ∑eE(A) f(e) + f(F). We assigned color wt (F) of local face antimagic total labeling that induces by proper edge coloring of G for each face. It is considered to be a local super antimagic total face coloring, if we give vertex labeling firts it call local super antimagic total face labeling. The local face super antimagic total chromatic number, denoted by γ lfat(G), is the minimum number of colors taken over all colorings induced by local super antimagic total face labelings of G. In this paper we study of local super antimagic total face chromatic number of graphs. Furthermore, we have determined exact value local super antimagic total face chromatic number of Shack(Cm, v, n), friendship graph Fn , fan graph Fn , and triangular ladder graph TLn .