{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:19Z","timestamp":1753893859156,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $G$ be a graph. Assume that $l$ and $k$ are two natural numbers. An $l$-sum flow on a graph\u00a0$G$ is an assignment of non-zero real numbers to the edges of $G$ such that for\u00a0every vertex $v$ of $G$ the sum of values of all edges\u00a0incidence with $v$ equals $l$. An $l$-sum $k$-flow is an $l$-sum flow with values from the set $\\{\\pm\u00a01,\\ldots ,\\pm(k-1)\\}$. Recently, it was proved that for every $r, r\\geq 3$, $r\\neq 5$, every $r$-regular\u00a0graph admits a $0$-sum $5$-flow.\u00a0In this paper we settle a conjecture by showing that every $5$-regular graph\u00a0admits a $0$-sum $5$-flow. Moreover, we prove that every $r$-regular graph of even order admits a $1$-sum $5$-flow.<\/jats:p>","DOI":"10.37236\/4986","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:06:08Z","timestamp":1578690368000},"source":"Crossref","is-referenced-by-count":4,"title":["0-Sum and 1-Sum Flows in Regular Graphs"],"prefix":"10.37236","volume":"23","author":[{"given":"S.","family":"Akbari","sequence":"first","affiliation":[]},{"given":"M.","family":"Kano","sequence":"additional","affiliation":[]},{"given":"S.","family":"Zare","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,5,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:28:14Z","timestamp":1579238894000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,27]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/4986","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,5,27]]},"article-number":"P2.37"}}