Zero-sum 6-flows in 5-regular graphs

2016/01/28 by Fan Yang, Yang, Fan, Xiangwen Li +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1601.07813

openalex publication_date 2016/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a graph. A zero-sum flow of G is an assignment of non-zero real numbers to the edges of G such that the sum of the values of all edges incident with each vertex is zero. Let k be a natural number. A zero-sum k-flow is a flow with values from the set \±1, …, ±(k - 1)\. In this paper, we prove that every 5-regular graph admits a zero-sum 6-flow.

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