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Browsing by Subject "spectrum problem"

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    Item type:Article, Access status: Open Access ,
    The spectrum problem for digraphs of order 4 and size 5
    (Wydawnictwa AGH, 2018) Bunge, Ryan C.; DeShong, Steven; El-Zanati, Saad Ibrahim; Fischer, Alexander; Roberts, Dan P.; Teng, Lawrence
    The paw graph consists of a triangle with a pendant edge attached to one of the three vertices. We obtain a multigraph by adding exactly one repeated edge to the paw. Now, let $D$ be a directed graph obtained by orientating the edges of that multigraph. For 12 of the 18 possibilities for $D$, we establish necessary and sufficient conditions on $n$ for the existence of a $(K^{*}_{n},D)$-design. Partial results are given for the remaining 6 possibilities for $D$.