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<p>In any connected graph, the sum of distances of a given vertex to all the other vertices is known as the transmission of that vertex. If any two distinct vertices have different transmissions in a connected graph, then this graph is said to be transmission irregular. We present an efficient algorithm that generates all the transmission irregular trees whose orders are within a given range, up to isomorphism. We subsequently use the developed algorithm to count the number of nonisomorphic transmission irregular trees of each order up to 42.</p>

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An efficient algorithm for generating transmission irregular trees

  • 期刊论文

  • 发表日期：

    2025年10月28日

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  • Ivan Stošić,
  • Ivan Damnjanović

摘要

In any connected graph, the sum of distances of a given vertex to all the other vertices is known as the transmission of that vertex. If any two distinct vertices have different transmissions in a connected graph, then this graph is said to be transmission irregular. We present an efficient algorithm that generates all the transmission irregular trees whose orders are within a given range, up to isomorphism. We subsequently use the developed algorithm to count the number of nonisomorphic transmission irregular trees of each order up to 42.