Local super anti-magic total face coloring on shackle graphs

Abstract

We define graph G as a nontrivial, finite, connected graph which contains vertex set V (G), edge set E(G), and face set F (G). We also define g as bijective function that mapping vertex, edge, and face labeling to natural number which starting from 1 until |V(G)| for vertex label, from |V(G)| + 1 until |V(G)| + |E(G)| for edge label, and the last for face label from |V (G)| + |E(G)| + 1 until |V (G)| + | E (G)| + |F(G)|. If there are different weights in any neighboring two faces f1 and f2 has w(f1) = w(f2) for f1, f2 G F (G), so g is considered a local super anti-magic total face labeling. A proper face coloring from local super anti-magic total face labeling caused by assigns the color of face weights to local super anti-magic total face coloring. The minimum number of colors needed for local super anti-magic total face coloring is called The chromatic number of the local super anti-magic total face coloring. γlatf (G) can be denoted as the chromatic number of the local super anti-magic total face coloring. Encryption keys can possibly be created from the result of local super anti-magic total face coloring that can be used to construct a modified Affine cipher and Cipher Feedback Mode. As a result, we have one the orem for the chromatic number of local super anti-magic total face coloring and two algorithms for establishing super anti-magic total face coloring on shackle graphs in Cipher Feedback Mode.