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The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four

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  • Kun Zhao
  • Shangzhao Li
  • Shaojun Dai
  • Ljubisa Kocinac

Abstract

The Merrifield–Simmons index iG of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, i.e., the number of independent vertex sets of G. In this paper, we determine the minimum Merrifield–Simmons index of unicyclic graphs with n vertices and diameter at most four.

Suggested Citation

  • Kun Zhao & Shangzhao Li & Shaojun Dai & Ljubisa Kocinac, 2021. "The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four," Journal of Mathematics, Hindawi, vol. 2021, pages 1-15, April.
    • Handle: RePEc:hin:jjmath:6680242
    DOI: 10.1155/2021/6680242
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