Sains Malaysiana 41(1)(2012): 129–131

Components in Graphs of Diagram Groups over the Union of Two Semigroup Presentations of Integers

(Kumpulan-Kumpulan Gambar Rajah Atas Kesatuan Dua  Persembahan Semikumpulan Bagi Integer)

Abd Ghafur Bin Ahmad

School of Mathematical, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600Bangi, Selangor, Malaysia

Yousof Gheisari

Department of Mathematics, Boushehr Branch, Islamic Azad University Boushehr, Iran

Received: 24 February 2011 / Accepted: 13 April 2011

ABSTRACT

Given any semigroup presentation, we may obtain the diagram group. The purpose of this paper is to determine the graphs Γn(P), (n ∈ N), which are obtained from diagram group for the union of two semigroup presentation of integers with s and t different initial generators. The number of vertices and edges in these graphs will be computed.

Keywords: Diagram groups; generators; initial generators; relation; semigroup presentation

ABSTRAK

Diberi sebarang persembahan semikumpulan, kita boleh peroleh kumpulan gambar rajah. Tujuan kertas ini ialah untuk menentukan graf-graf Γn(P), (n ∈ N) yang diperoleh daripada kumpulan gambar rajah untuk kesatuan dua persembahan semikumpulan dengan s dan t penjana awal yang berbeza. Bilangan bucu dan tepi dalam graf-graf ini akan dihitung.

Kata kunci: Hubungan; kumpulan gambar rajah; penjana; penjana awal; persembahan semikumpulan

REFERENCES

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Gheisari, Y. & Ahmad, A.G.B. 2010. General polynomial for component of graphs from diagram group of semigroup presentation P = 〈x, y, z|x = y, y = z, z = z〉. Journal of International Mathematical Forum 18: 875-880.

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*Corresponding author; email: ghafur@ukm.my