Opuscula Mathematica
Opuscula Math. 38, no. 1 (), 15-30
https://doi.org/10.7494/OpMath.2018.38.1.15
Opuscula Mathematica

The spectrum problem for digraphs of order 4 and size 5







Abstract. 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 \(D\).
Keywords: spectrum problem, digraph decompositions.
Mathematics Subject Classification: 05C20, 05C51.
Cite this article as:
Ryan C. Bunge, Steven DeShong, Saad I. El-Zanati, Alexander Fischer, Dan P. Roberts, Lawrence Teng, The spectrum problem for digraphs of order 4 and size 5, Opuscula Math. 38, no. 1 (2018), 15-30, https://doi.org/10.7494/OpMath.2018.38.1.15
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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