Flow number of signed Halin graphs

Xiao Wang, You Lu and Shenggui Zhang

Applied Mathematics and Computation, 2021, vol. 393, issue C

Abstract: The flow number of a signed graph (G,Σ) is the smallest positive integer k such that (G,Σ) admits a nowhere-zero integer k-flow. In 1983, Bouchet (JCTB) conjectured that every flow-admissible signed graph has flow number at most 6. This conjecture remains open for general signed graphs even for signed planar graphs. A Halin graph is a plane graph consisting of a tree without vertices of degree two and a circuit connecting all leaves of the tree. In this paper, we prove that every flow-admissible signed Halin graph has flow number at most 5, and determine the flow numbers of signed Halin graphs with a (3,1)-caterpillar tree as its characteristic tree.

Keywords: Nowhere-zero integer flow; Flow number; Signed graph; Halin graph (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:393:y:2021:i:c:s0096300320307049

DOI: 10.1016/j.amc.2020.125751

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