On Rainbow Vertex Antimagic Coloring of Shell Related Graphs
Agnes Ayu Utami Ulya Kamila, Dafik Dafik, Arika Indah Kristiana, Rosanita Nisviasari, Elsa Yuli Kurniawati · Advances in physics research/Advances in Physics Research · 2023
A rainbow vertex antimagic coloring namely rainbow vertex coloring and antimagic labeling.For a bijective functionThe function f is known as vertex antimagic labeling if every vertex has a distinct weight.Any path P in a graph G labeled with edges called a rainbow path if any two interior vertices on the path u -v have different weights.If there is a rainbow path u -v between every pair of u and v vertices, then f is referred to as the rainbow vertex antimagic labeling of G. Graph G is called rainbow vertex antimagic coloring when each u -v edge has a vertex weight color wf (v).The deductive analytic method is used in this research to analyze the issues that have been discovered, define the issue, and demonstrate patterns and theorems.With n ranging, the steps required are to draw a graph, determine the cardinality, search for the pattern of the rainbow vertex connection number as the lower bound, construct the bijective function to obtain the upper bound, and if the upper bound meets the lower bound, than new theorems and their proofs will be generated.Using the results of the proven theorem analysis will form a conclusion.BF (n, m) and shell flower graph [Cn,n-3, k2] k