@article{MAKHILLJEAS2019142118610,
    title = {On Cyclic Triple System and Factorization},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {14},
    number = {21},
    pages = {7928-7933},
    year = {2019},
    issn = {1816-949x},
    doi = {jeasci.2019.7928.7933},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2019.7928.7933},
    author = {Mowafaq,Sharmila and},
    keywords = {near-k-factor,Triple system,factorization,demonstrate,starter triples,complete multigraph},
    abstract = {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).}
    }