TY  - JOUR
ID  - Bunge2018
LB  - Bunge2018
AU  - Bunge, Ryan C.
AU  - DeShong, Steven
AU  - El-Zanati, Saad I.
AU  - Fischer, Alexander
AU  - Roberts, Dan P.
AU  - Teng, Lawrence
TI  - The spectrum problem for digraphs of order 4 and size 5
ST  - The spectrum problem for digraphs of order 4 and size 5
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2018
VL  - 38
IS  - 1
SP  - 15
EP  - 30
DO  - https://doi.org/10.7494/OpMath.2018.38.1.15
UR  - https://doi.org/10.7494/OpMath.2018.38.1.15
AB  - 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 \(D\).
KW  - spectrum problem
KW  - digraph decompositions
SN  - 1232-9274
ER  -