Extending Extremal Polygonal Arrays for the Merrifield-Simmons Index

  • Guillermo De Ita Luna
  • J. Raymundo Marcial-RomeroEmail author
  • J. A. Hernández
  • Rosa Maria Valdovinos
  • Marcelo Romero
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10267)


Polygonal array graphs have been widely investigated, and they represent a relevant area of interest in mathematical chemistry because they have been used to study intrinsic properties of molecular graphs. For example, to determine the Merrifield-Simmons index of a polygonal array \(A_n\) that is the number of independent sets of that graph, denoted as \(i(A_n)\).

In this paper we consider the problem of extending an initial polygonal array \(A_n\) adding a new polygon p to form \(A_{n+1}\), for minimizing or maximizing the Merrifield-Simmons index \(i(A_{n+1}) = i(A_n \cup p)\). Our method does not require to compute \(i(A_n)\) or \(i(A_n \cup p)\), explicitly.


Counting the number of independent sets Enumerative algorithms Efficient counting Merrifield-Simmons index 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Guillermo De Ita Luna
    • 1
  • J. Raymundo Marcial-Romero
    • 2
    Email author
  • J. A. Hernández
    • 2
  • Rosa Maria Valdovinos
    • 2
  • Marcelo Romero
    • 2
  1. 1.Facultad de Ciencias de la Computación, BUAPPueblaMexico
  2. 2.Facultad de Ingeniería, UAEMTolucaMexico

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