Hasil Kali Matriks (Mod 2) pada Graf Roda, Graf Pertemanan dan Graf Bunga

Fransiskus Fran; Novita Indah Saputri; Mariatul Kiftiah

doi:10.34312/jjom.v3i2.10468

Hasil Kali Matriks (Mod 2) pada Graf Roda, Graf Pertemanan dan Graf Bunga

Fransiskus Fran, Novita Indah Saputri, Mariatul Kiftiah

Abstract

ABSTRAK

Pada artikel ini dibahas sifat-sifat hasil kali matriks (mod 2) terkait graf roda, graf pertemanan, dan graf bunga yang grafikal. Beberapa hasil yang diperoleh, A(Wn)A(Wn)(Mod 2) dan A(Wn)A(Sn)(Mod 2) grafikal apabila n=2k+1 dengan Sn merupakan graf bintang. Selanjutnya, diperoleh A(Wn)A(Go)(mod 2) dan A(Wn)A(G0)(mod 2) grafikal untuk semua n>=3 dengan G0 adalah subgraf dari Wn dengan degG0v0=0, degG0vl=degWnvl, untuk 1<= l <= n. Hasil kali matriks (mod 2) yang grafikal juga diperoleh untuk graf pertemanan dan graf bunga dengan komplemen dan subgrafnya masing- masing. Hasil lebih umum diperoleh untuk kondisi sehingga A(G)A(G)(mod 2) grafikal.

ABSTRACT

In this paper, we discussed the properties of the wheel, flower and friendship graphs for which the matrix product under modulo 2 was graphical. Let Sn be a star graph and G0 be a subgraph of Wn where degG0v0=0, degG0vl=degWnvl, for 1<= l <= n. We proved the matrix product A(Wn)A(Wo)(mod 2) and A(Wn)A(Sn)(Mod 2) was graphical for n=2k+1 and the matrix product A(Wn)A(Go)(mod 2) and A(Wn)A(G0)(mod 2) was graphical for all n>=3. For the next, a graphical matrix product (mod 2) was also obtained for the friendship graph and the flower graph with its complement and subgraph, respectively. As more general results were obtained for conditions such that A(G)A(G)(mod 2) was graphical.

Keywords

Adjacency Matrix; Subgraph; Wheel Graph; Flower Graph; Friendship Graph; Matrix Product

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DOI: https://doi.org/10.34312/jjom.v3i2.10468