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<p>Closeness is a key structural measure used to evaluate the significance of a node in a network. An Eulerian cycle is a closed walk that visits every edge in a graph exactly once. A graph containing an Eulerian cycle is called an Eulerian graph. This paper addresses the problem of determining the graphs that maximize and minimize the closeness among Eulerian graphs of a fixed order. Specifically, we identify and characterize the graphs that achieve the maximum and minimum closeness values, respectively, within the class of Eulerian graphs of a given order.</p>

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Eulerian Graphs with Extremal Closeness

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • Fazal Hayat,
  • Shou-Jun Xu

摘要

Closeness is a key structural measure used to evaluate the significance of a node in a network. An Eulerian cycle is a closed walk that visits every edge in a graph exactly once. A graph containing an Eulerian cycle is called an Eulerian graph. This paper addresses the problem of determining the graphs that maximize and minimize the closeness among Eulerian graphs of a fixed order. Specifically, we identify and characterize the graphs that achieve the maximum and minimum closeness values, respectively, within the class of Eulerian graphs of a given order.