On Local Vertex Antimagic Total Coloring Of Path, Cycle, And Star Graphs With Comb Operation
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https://doi.org/10.32665/james.v8i2.4777Keywords:
Chromatic Number, Cycle Graph, Local Vertex Antimagic Total, Path Graph, Star GraphAbstract
Let G(V,E) be a graph consisting of a set of vertices V(G) and a set of edges E(G) where the number of vertices and edges are denoted by |V(G)| and |E(G)|, respectively. A bijective function f:V(G) \vee E(G) \to {1,2,3,...,(|V(G)|+|E(G)|)} is defined as a local vertex antimagic total coloring if there exist two adjacent vertex vx and vy with . Therefore, every local vertex antimagic total coloring produces a vertex coloring of the graph G, where each vertex v is assigned a color corresponding to its weight w(v). This research is essential as it contributes to development of graph coloring theory, particularly in the area of local vertex antimagic total coloring, which has been rarely studied. This research discusses the local vertex antimagic total coloring of and which aims to determine the chromatic number. The result of the research is the chromatic number of local vertex antimagic total coloring of and the chromatic number of local vertex antimagic total coloring , is if is odd and if is even.References
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