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<p>A diametral path of a graph is the geodesic path whose length is equal to the diameter of the graph. Trees having exactly one diametral path are characterised. A maximal path is a path that is not contained in any longer path. We introduce maximal path decomposition as the collection of edge-disjoint maximal paths. We characterise trees that admit maximal path decomposition. An algorithm is developed that outputs the maximal path decompositions and finds the number of maximal path decompositions.</p>

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Characterisation of Trees with Exactly One Diametral Path

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • B. M. Abhinaya,
  • Tabitha Agnes Mangam

摘要

A diametral path of a graph is the geodesic path whose length is equal to the diameter of the graph. Trees having exactly one diametral path are characterised. A maximal path is a path that is not contained in any longer path. We introduce maximal path decomposition as the collection of edge-disjoint maximal paths. We characterise trees that admit maximal path decomposition. An algorithm is developed that outputs the maximal path decompositions and finds the number of maximal path decompositions.