Multiplisitas sikel graf commuting dan noncommuting grup dihedral

INDONESIA:

Sikel adalah jalan tertutup tak trivial yang setiap titiknya berbeda. Multiplisitas sikel adalah maksimal banyaknya sikel dari suatu graf yang sisi-sisinya saling lepas.

Metode penelitian yang digunakan dalam peneltian ini adalah studi kepustakaan dengan tahapan analisis yang diawali dengan memberikan grup dihedral dan menentukan elemen-elemengrup dihedral-2ndengan 3≤n≤8, kemudian hasil operasi komposisi antar elemen disajikan dalam bentuk table Cayley, selanjutnya mencari elemen-elemen yang komutatif dan yang tidak komutatif, menggambarkan graf commuting(C(D_2n)) dan graf noncommuting(NC(D_2n))dari grup dihedral, selanjutnya mencari pola multiplisitas sikel, dan membangun suatu teorema beserta pembuktiannya. Hasil penelitian ini adalah:

1.Multiplisitas sikel graf commuting grup dihedral adalah...

2.Multiplisitas sikel graf noncommuting grup dihedral adalah...

Bagi penelitian selanjutnya diharapkan dapat menemukan bermacam-macam teorema tentang graf commuting dan noncommuting dari grup lainnya.

ENGLISH:

Cycle is non-trivial closed path which all of the vertices are distinct. Then cycle multiplicity is the maximum number of edge disjoint cycle in a graph.

The research method that used in this research is literature study with analysis phase. It begins by giving a dihedral grup and determining the elements of the dihedral-2n group, which 3≤n≤8, then the resulting of elements composition operation is presented using Cayle’s table. The next step is determining the commutative and noncommutative elements, and then figuring commuting graph (C(D_2n )) and noncommuting graph (NC(D_2n )) from dihedral group. From this step we can observe the model of cycle multiplicity, forming the theorems and its proof. The results of this research are:
1.The cycle multiplicity of commuting graph of dihedral group...

2.The cycle multiplicity of noncommuting graph of dihedral group...

This research can be continued for cycle multiplicity of another graph. And the another hopes that the further research can determine another theorem of commuting and noncommuting from another groups.