Automorfisma Graf Kipas Angin

Abstract

This study discusses automorphisms in fan graphs, which are formed by combining a friendship graph Fn and a path graph pm, with one of the end vertices in the path graph pm directly connected to the central vertex of Fn. The main objective of this study is to determine the number of automorphisms of the fan graph Fnpm and to examine whether the automorphisms of the fan graph Fnpm form a group. The method used in this study is literature review. Based on the characteristics of the fan graph, it was found that automorphisms only occur in the triangular part of the graph Fn, whereas the path pm has only the identity automorphism due to restrictions in vertex swapping. The results of the study show that the number of automorphisms of the fan graph Fnpm is 2n.n! for n ≥2, and the automorphisms of the fan graph Fnpm form a group.