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On 1-sum flows in undirected graphs
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2016 (English)In: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 31, 646-665 p.Article in journal (Refereed) Published
Abstract [en]

Let G = (V, E) be a simple undirected graph. For a given set L subset of R, a function omega: E -> L is called an L-flow. Given a vector gamma is an element of R-V , omega is a gamma-L-flow if for each v is an element of V, the sum of the values on the edges incident to v is gamma(v). If gamma(v) = c, for all v is an element of V, then the gamma-L-flow is called a c-sum L-flow. In this paper, the existence of gamma-L-flows for various choices of sets L of real numbers is studied, with an emphasis on 1-sum flows. Let L be a subset of real numbers containing 0 and denote L* := L \ {0}. Answering a question from [S. Akbari, M. Kano, and S. Zare. A generalization of 0-sum flows in graphs. Linear Algebra Appl., 438:3629-3634, 2013.], the bipartite graphs which admit a 1-sum R* -flow or a 1-sum Z* -flow are characterized. It is also shown that every k-regular graph, with k either odd or congruent to 2 modulo 4, admits a 1-sum {-1, 0, 1}-flow.

Place, publisher, year, edition, pages
INT LINEAR ALGEBRA SOC , 2016. Vol. 31, 646-665 p.
Keyword [en]
L-Flow, gamma-L-Flow, c-Sum flow, Bipartite graph
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-134293DOI: 10.13001/1081-3810.3003ISI: 000396550500002OAI: oai:DiVA.org:umu-134293DiVA: diva2:1094202
Available from: 2017-05-09 Created: 2017-05-09 Last updated: 2017-05-09Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • de-DE
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