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

Funding Information:
The authors are much grateful to the anonymous referee for their valuable comments on our paper, which have considerably improved the presentation of this paper. K. C. Das is supported by National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050646 ).

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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