On the Merrifield–Simmons index of tricyclic graphs

Kinkar Chandra Das, Suresh Elumalai, Surojit Ghosh, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


The total number of independent subsets, including the empty set, of a graph, is also termed as the Merrifield–Simmons index (MSI) in mathematical chemistry. Zhu and Yu (2012) presented a lower bound on Merrifield–Simmons index of tricyclic graphs in terms of order n and the characterization of extremal graphs. This result was erroneous. In this paper, we correct this result. Moreover, we characterize the tricyclic graphs on n vertices with the second and third smallest values of the Merrifield–Simmons index.

Original languageEnglish
Pages (from-to)342-354
Number of pages13
JournalDiscrete Applied Mathematics
StatePublished - 15 Dec 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier B.V.


  • Fibonacci number
  • Independent set
  • Merrifield–Simmons index
  • Tricyclic graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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