On conjecture of Merrifield–Simmons index

Kinkar Chandra Das, Suresh Elumalai, Arpita 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. The eccentric complexity of a graph G is defined to be the number of different eccentricities of its vertices. Hua et al. (2020) mentioned two open problems and a conjecture on the Merrifield–Simmons index and eccentric complexity of graph. In this paper we solve both open problems and a conjecture. Moreover, we generalize some of the results.

Original languageEnglish
Pages (from-to)211-217
Number of pages7
JournalDiscrete Applied Mathematics
StatePublished - 15 Jan 2021

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.


  • Diameter
  • Eccentric complexity
  • Graph
  • Independence number
  • Merrifield–Simmons index

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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