Discrete Mathematics ( IF 0.770 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.disc.2020.112074 S. Akbari; H.R. Maimani; Leila Parsaei Majd; I.M. Wanless
Given a - design, , a zero-sum -flow of is a map such that for any point , the sum of over all blocks incident with is zero. For a positive integer , we find a zero-sum -flow for an and for an for , if there are , and such that the and both have a zero-sum -flow. In 2015, it was conjectured that for every admits a zero-sum 3-flow. Here, it is shown that many cyclic have a zero-sum 3-flow. Also, we investigate the existence of zero-sum flows for some Steiner quadruple systems.