Automorfisma Graf Kupu-kupu

Abstract

An automorphism of a graph G is an isomorphism of the graph G to itself, which is a bijective mapping that preserves adjacency between the vertices in the graph G. This study focuses on the generalized butterfly graph, denoted as BFn, which is generated by inserting vertices into all wings with the same number of insertions. The graph BFn has 2n + 1 vertices and 4n − 2 edges, with the vertex set V (BFn) = {vi | i = 0, 1, 2, . . . , 2n}and the edge set E(BFn) = (vi , vi+1) | i = 1, 2, . . . , n − 1, n + 1, . . . , 2n − 1 ∪ (v0, vi) | i = 1, 2, . . . , 2n. The results of this study show that there are exactly 2 automorphisms when (n = 1), and 8 automorphisms for each (n ≥ 2). This study also proves that the set of all automorphisms of the butterfly graph BFn can form a group, known as the automorphism group.