Jurnal Ilmu Dasar
Vol 10 No 2 (2009)

Embedding K2,3,m Graphs on Torus

Liliek Susilowati (Departemen Matematika, FSaintek Universitas Airlangga)



Article Info

Publish Date
02 Jul 2009

Abstract

 This script aim to determine the maximal value of m of K2,3,m graph so that can be redrawn on torus without intersection of edges. Hereinafter, will be determined the toroidal crossing number of  K2,3,m which nontoroidal by the m minimize. To determined if the  K2,3,m graph is toroidal, it is enough with drawn the graph on torus without intersection of edges, whereas, to determined if it is nontoroidal, besides with drawn, is also needed by theorem about properties of graph that containing K5-subdivision. Then to determined the toroidal crossing number was used the technique by proof of the crossing number of  K2,2,3 and looked for of all probabilities of the edges is going to intersect. In this research, was obtained the result that maximal value of m of  K2,3,m so that can be drawn on torus without intersection of edges is 3, while the toroidal crossing number of  K2,3,4 is 2, and our conjecture is tcr().

Copyrights © 2009






Journal Info

Abbrev

JID

Publisher

Subject

Control & Systems Engineering Mathematics

Description

Jurnal ILMU DASAR (JID) is a national peer-reviewed and open access journal that publishes research papers encompasses all aspects of natural sciences including Mathematics, Physics, Chemistry and Biology. JID publishes 2 issues in 1 volume per year. First published, volume 1 issue 1, in January ...