TY  - JOUR
T1  - On Cyclic Triple System and Factorization
AU - Alqadri, Mowafaq AU - Karim, Sharmila AU - Ibrahim, Haslinda 
JO  - Journal of Engineering and Applied Sciences
VL  - 14
IS  - 21
SP  - 7928
EP  - 7933
PY  - 2019
DA  - 2001/08/19
SN  - 1816-949x
DO  - jeasci.2019.7928.7933
UR  - https://makhillpublications.co/view-article.php?doi=jeasci.2019.7928.7933
KW  - near-k-factor
KW  -Triple system
KW  -factorization
KW  -demonstrate
KW  -starter triples
KW  -complete multigraph
AB  - A near-k-factor of a graph G is a spanning subgraph in which exactly one isolated vertex and all other
vertices of order k. In this study, we employ the near-four-factor concept and (m<sub>1</sub>, m<sub>2</sub>, &#133;, m<sub>r</sub>)-cycle system to present a new method for constructing a cyclic 12-fold triple system. Firstly, we would like to propose a new
type of cyclic triple system called cyclic triple near factorization, denoted by CTNF(&#965;). Then, we prove the
existence of CTNF(&#965;) along with an algorithm for starter triples of CTNF(&#965;) for &#965; = 12n+2 when, n is even.
Finally, we use the construction of CTNF(&#965;) to demonstrate the existence of [a, b] factorization of 12 K<sub>&#965;</sub> for a 
a = 8 and b = 4 (&#965;-1).
ER  -