The spectrum problem for digraphs of order 4 and size 5

Autor: Ryan C. Bunge, Steven DeShong, Saad I. El-Zanati, Alexander Fischer, Dan P. Roberts, Lawrence Teng
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Zdroj: Opuscula Mathematica, Vol 38, Iss 1, Pp 15-30 (2018)
Druh dokumentu: article
ISSN: 1232-9274
DOI: 10.7494/OpMath.2018.38.1.15
Popis: 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 \(D\).
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