Journal of Mathematical Chemistry

, Volume 57, Issue 2, pp 609–615 | Cite as

Inverse problem for Zagreb indices

  • Aysun Yurtas
  • Muge Togan
  • Veerebradiah Lokesha
  • Ismail Naci Cangul
  • Ivan GutmanEmail author
Original Paper


The inverse problem for integer-valued topological indices is about the existence of a graph having its index value equal to a given integer. We solve this problem for the first and second Zagreb indices, and present analogous results also for the forgotten and hyper-Zagreb index. The first Zagreb index of connected graphs can take any even positive integer value, except 4 and 8. The same is true if one restricts to trees or to molecular graphs. The second Zagreb index of connected graphs can take any positive integer value, except 2, 3, 5, 6, 7, 10, 11, 13, 15 and 17. The same is true if one restricts to trees or to molecular graphs.


Zagreb index First Zagreb index Second Zagreb index Forgotten index Hyper-Zagreb index 

Mathematics Subject Classification

Primary 05C09 Secondary 05C90 



This work was supported by the research fund of Uludag University, Project No. F-2015/17.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Aysun Yurtas
    • 1
  • Muge Togan
    • 1
  • Veerebradiah Lokesha
    • 2
  • Ismail Naci Cangul
    • 1
  • Ivan Gutman
    • 3
    Email author
  1. 1.Mathematics Department, Faculty of Arts and ScienceUludag UniversityGorukle, BursaTurkey
  2. 2.Department of Studies in MathematicsVijayanagara Sri Krishnadevaraya UniversityBallariIndia
  3. 3.Faculty of ScienceUniversity of KragujevacKragujevacSerbia

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