Opuscula Mathematica
Opuscula Math. 38, no. 1 (2018), 15-30

The spectrum problem for digraphs of order 4 and size 5

Ryan C. Bunge
Steven DeShong
Saad I. El-Zanati
Alexander Fischer
Dan P. Roberts
Lawrence Teng
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.
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About the authors ▼
Ryan C. Bunge
Illinois State University, Normal, IL 61790-4520, USA
Steven DeShong
Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
Saad I. El-Zanati
Illinois State University, Normal, IL 61790-4520, USA
Alexander Fischer
Jacobs High School, Algonquin, IL 60102, USA
Dan P. Roberts
Illinois Wesleyan University, Bloomington, IL 61701, USA
Lawrence Teng
University of Michigan, Ann Arbor, MI 48109, USA
About the article ▼
Communicated by Mariusz Meszka.
Received: 2016-01-05.
Revised: 2017-06-06.
Accepted: 2017-06-14.
Published online: 2017-11-13.
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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