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<p>The path decomposition of a graph <i>G</i> is the process of decomposing it into edge-disjoint paths. An induced signed graph is a signed graph formed from an ordinary unsigned graph by assigning signs to its edges according to some protocol. In this paper, we introduce the notion of a path-induced signed graph as an induced signed graph whose edges receive a sign according to whether its end vertices are the end vertices of a path in a path decomposition of <i>G</i>. We also discuss some characteristics of this type of signed graph.</p>

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On path-induced signed graphs

  • 期刊论文

  • 发表日期：

    2026年2月27日

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  • Jomon Kottarathil,
  • Sudev Naduvath

摘要

The path decomposition of a graph G is the process of decomposing it into edge-disjoint paths. An induced signed graph is a signed graph formed from an ordinary unsigned graph by assigning signs to its edges according to some protocol. In this paper, we introduce the notion of a path-induced signed graph as an induced signed graph whose edges receive a sign according to whether its end vertices are the end vertices of a path in a path decomposition of G. We also discuss some characteristics of this type of signed graph.