The spectrum problem for digraphs of order 4 and size 5 | Zendy

Ryan C. Bunge | Zendy; Steven DeShong | Zendy; Saad I. ElZanati | Zendy; Alexander Fischer | Zendy; Dan Roberts | Zendy; Lawrence Teng | Zendy

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The spectrum problem for digraphs of order 4 and size 5

Author(s) -

Ryan C. Bunge,

Steven DeShong,

Saad I. ElZanati,

Alexander Fischer,

Dan Roberts,

Lawrence Teng

Publication year - 2017

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2018.38.1.15

Subject(s) - multigraph , mathematics , combinatorics , graph , order (exchange) , enhanced data rates for gsm evolution , spectrum (functional analysis) , discrete mathematics , computer science , artificial intelligence , physics , finance , quantum mechanics , economics

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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