1. Inverse problem for Zagreb indices
- Author
-
Ivan Gutman, Ismail Naci Cangul, Aysun Yurtas, V. Lokesha, Muge Togan, Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Yurttaş, Aysun, Togan, Müge, Cangül, İsmail Naci, ABA-6206-2020, J-3505-2017, and AAG-8470-2021
- Subjects
Hyper-Zagreb index ,Topological indexes ,010304 chemical physics ,Applied Mathematics ,010102 general mathematics ,Zagreb index ,Mathematics, interdisciplinary applications ,General Chemistry ,Inverse problem ,01 natural sciences ,Chemistry, multidisciplinary ,Graph ,Combinatorics ,Chemistry ,Unicyclic Graph ,Vertex Degree ,Integer ,0103 physical sciences ,Forgotten index ,Secondary 05C90 ,First Zagreb index ,0101 mathematics ,Second Zagreb index ,Primary 05C09 ,Mathematics - Abstract
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.
- Published
- 2018