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<p>The Merrifield-Simmons index (MSI) is the count of independent subsets of a graph, including the empty set. The connective eccentricity index (CEI) is the eccentricity-based topological index. This work provides a comparative analysis of the MSI and the CEI for several graphs with various parameters. We examine the edge interval in graphs with different independence numbers, where the MSI is greater than the CEI in certain cases and smaller in others. We also explore an edge limit where the MSI exceeds the CEI if the size of the graph is below the limit. Otherwise, the relationship between both indices is determined by several parameters other than size. Finally, we examine the relationship between the MSI and the CEI of product graphs, considering their specific independence numbers and diameter.</p>

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On the comparative analysis of Merrifield-Simmons index and connective eccentricity index

  • 期刊论文

  • 发表日期：

    2025年4月11日

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  • Mital Gor,
  • S. Veeramani

摘要

The Merrifield-Simmons index (MSI) is the count of independent subsets of a graph, including the empty set. The connective eccentricity index (CEI) is the eccentricity-based topological index. This work provides a comparative analysis of the MSI and the CEI for several graphs with various parameters. We examine the edge interval in graphs with different independence numbers, where the MSI is greater than the CEI in certain cases and smaller in others. We also explore an edge limit where the MSI exceeds the CEI if the size of the graph is below the limit. Otherwise, the relationship between both indices is determined by several parameters other than size. Finally, we examine the relationship between the MSI and the CEI of product graphs, considering their specific independence numbers and diameter.