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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

The spectrum problem for some digraphs of order 4 and size 6

Bunge, Ryan C. 1, El-Zanati, Saad I. 1, Hawken, Kerry A. 2, Ramírez, Esteban 3, Roberts, Dan P. 4, Rodríguez-Guzmán, Emmanuel 5, Williams, Jesse D. jun. 1
1Illinois State University, Normal, IL 61790-4520, USA
2Ball State University, Muncie, IN 47306, USA
3Governors State University, University Park, IL 60484, USA
4Illinois Wesleyan University, Bloomington, IL 61701, USA
5CeDIn-Universidad Interamericana, San Juan, PR 00919, USA

Abstract

Consider the multigraph obtained by adding a double edge to \( K_4 – e \). Now, let \( D \) be a directed graph obtained by orientating the edges of that multigraph. We establish necessary and sufficient conditions on \( n \) for the existence of a \( (K^*_n, D) \)-design for four such orientations.

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Citation
Bunge, Ryan C., El-Zanati, Saad I., Hawken, Kerry A., Ramírez, Esteban, Roberts, Dan P., Rodríguez-Guzmán, Emmanuel, Williams, Jesse D. jun.. The spectrum problem for some digraphs of order 4 and size 6[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 114. 293-306. .