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.

On the rainbow antimagic coloring of vertex amalgamation of graphs

“…The antimagic labeling of trees has been discovered by Liang et al [20]. More study of antimagic labeling some graphs in [5,15,21,23].…”

Pewarnaan Lokal Wilayah Super Antimagic Total Pada Graf Tangga dan Graf Tiga Tangga Melingkar

“…Pewarnaan antimagic telah banyak diteliti oleh para peneliti-peneliti sebelumnya seperti [5], [6], [7] dan [8] yang meneliti pewarnaan titik antimagic, [9], [10], [11] dan [12] yang meneliti pewarnaan lokal sisi antimagic, [13] dan [14] yang meneliti pewarnaan lokal wilayah antimagic dan masih banyak lagi peneliti yang meneliti pewarnaan lokal antimagic. Pada hasil pewarnaan lokal antimagic sebelumnya, untuk pewarnaan lokal wilayah super antimagic total dari graf tangga dan graf tiga tangga melingkar belum diteliti oleh peneliti sebelumnya.…”