Combinatorial Properties of Modified Chordal Rings Degree Four Networks
R. N. Farah, O. Othman and M. H. Selamat
DOI : 10.3844/jcssp.2010.279.284
Journal of Computer Science
Volume 6, Issue 3
Problem statement: Modified Chordal Rings Degree Four, called CHRm4 is the first modified structure of chordal rings. This CHRm4 is an undirected circulant graph and is a double loop graph. Approach: This study presented the main properties of CHRm4. There are connectivity, Hamiltonian cycle and asymmetric. Results: Several definitions, postulates, corollary, theorems and lemmas were constructed according to these three main properties. It is about interconnection between nodes, how the Hamiltonian cycle was occurred and why CHRm4 is not symmetric. Conclusion: From these three properties, there are two dominant properties obviously shown that the CHRm4 is contrary from the previous traditional Chordal Rings Degree Four (CR4). It is connectivity and asymmetric. There are different connections for odd and even nodes, therefore CHRm4 is not symmetric. The Hamiltonian cycle property has the same concept with CR4.
© 2010 R. N. Farah, O. Othman and M. H. Selamat. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.