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

Abstract

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 F1 and F2, wt(F1) ≠ wt(F2), where F ∈ G, wt(F) = ∑vϵV(A)f(v) + ∑eϵE(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 γlfat(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.