Local super antimagic total face coloring of planar graphs

Abstract

We using graph G = (V(G), E(G), F(G)) be a nontrivial, finite, connected graph, and a g bijective function mapping total labeling of graph to natural number start form 1 until the sum of vertices, edge, and faces. The sum of vertices, edges, and faces labels in a face f is called the weight of the face f ∈ F(G). If any adjacent two faces f 1 and f 2 have different weights w(f 1) ≠ w(f 2) for f 1, f 2 ∈ F(G), then g is called a labeling of local antimagic total face. We call labeling of local antimagic total face is super if we add vertices label start from 1 until the sum of vertices, edges label start from the sum of vertices plus 1 until the sum of vertices and edges, and faces label start form the sum of vertices and edges plus one untul the sum of vertices, edges, and faces. The local super antimagic total face labeling that induces a proper faces coloring of G where the faces f is assigned by the color w(f) is called local super antimagic total face coloring. The minimum number of colors in local super antimagic total face coloring is local antimagic total face chromatic number and denoted by γ latf (G). In this paper, we used some planar graph such as wheel graph (Wn ), jahangir graph (J(2, n)), ladder graph (Ln ), and circular ladder graph (CLn ). Our results attained the lower bound of local super antimagic total face chromatic number.