@article{MAKHILLJEAS2020151119313,
    title = {On Cyclic Butterfly k-Cycle Decomposition of the 2-Fold Complete Graph},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {15},
    number = {11},
    pages = {2426-2433},
    year = {2020},
    issn = {1816-949x},
    doi = {jeasci.2020.2426.2433},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2020.2426.2433},
    author = {Raja’i,Haslinda and},
    keywords = {2-fold complete graph,k-cycle decomposition,path cover,near-2-factor,difference system},
    abstract = {In this study, we employ the near-twofactorization
to develop a new type of simple k-cycle
decomposition of the 2-fold complete graph 2K<sub>v</sub>, called a
Butterfly k-cycle decomposition of 2K<sub>v</sub>. Especially, we
focus on proving the existence of cyclic Butterfly
(v-1/2)-cycle decomposition of 2K<sub>v</sub> for the case v / 3
(mod 12) using the difference method for constructing the
starter cycles.}
    }