Automorfisma Graf Bunga Matahari

Abstract

A graph automorphism is an isomorphism from a graph $G$ to itself a function that maps a graph to itself one-on-one and onto, and preserves the adjacency relation between the vertices of the graph, if two vertices are connected by an edge, then the result of their mapping must also be connected. Sunflower Graph, denoted by $SF_n$, is a simple undirected graph consisting of a center vertex $v_0$, a cycle vertex $C_n$ with vertices $v_0, v_1, \dots, v_n$, and additional vertices $v_{n+1}, v_{n+2}, v_{n+3}, \dots, v_{n+i}$. Each vertex $v_n$ is also connected to the center vertex $v_0$. There are a total of $2n+1$ vertices and $4n$ edges, with a center vertex of degree $n$, an inner cycle vertex $v_n$ of degree 5, and an outer vertex $v_{2n}$ of degree 2. The results show that the total number of automorphism functions on the Sunflower Graph $SF_n$ is $2n$, for $n > 2$, and the automorphism group of the Sunflower Graph $SF_n$ is the dihedral group of order $2n$, denoted by $D_{2n}$.