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<p>The distance of a vertex in a graph is the sum of distances from that vertex to all other vertices of the graph. The Wiener index of a graph is the sum of distances between all its unordered pairs of vertices. A graph has been obtained that contains a vertex achieving the maximum distance among all graphs on <i>n</i> vertices with fixed number of cut vertices. Further, the graphs having maximum Wiener index among all graphs on <i>n</i> vertices with at most 3 cut vertices have been characterised.</p>

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On vertex peripherians and Wiener index of graphs with fixed number of cut vertices

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Dinesh Pandey

摘要

The distance of a vertex in a graph is the sum of distances from that vertex to all other vertices of the graph. The Wiener index of a graph is the sum of distances between all its unordered pairs of vertices. A graph has been obtained that contains a vertex achieving the maximum distance among all graphs on n vertices with fixed number of cut vertices. Further, the graphs having maximum Wiener index among all graphs on n vertices with at most 3 cut vertices have been characterised.