Raja’i  Aldiabat, Haslinda  Ibrahim, Sharmila  Karim, 
    On Cyclic Butterfly k-Cycle Decomposition of the 2-Fold Complete Graph,
    Journal of Engineering and Applied Sciences,
    Volume 15,Issue 11,
    2020,
    Pages 2426-2433,
    ISSN 1816-949x,
    jeasci.2020.2426.2433,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2020.2426.2433)
    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.
    Keywords: 2-fold complete graph;k-cycle decomposition;path cover;near-2-factor;difference system