Some chemical indices related to the number of triangles

Document Type : Research Paper


School of Mathematical Sciences, Xiamen University, 361005, Fuzhou, Xiamen, P. R. China.


Many chemical indices have been invented in theoretical chemistry, such as the Zagreb index, the Lanzhou index, the forgotten index, the Estrada index etc. In this paper, we show that the first Zagreb index is only related to the sum of the number of triangles in a graph and the number of triangles in its complement. Moreover, we determine the sum of the first and second Zagreb index, the Lanzhou index and the forgotten index for a graph and its complement in terms of the number of triangles in a graph and the number of triangles in its complement. Finally, we estimate the Estrada index in terms of order, size, maximum degree and the number of triangles.


Main Subjects

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  • Receive Date: 10 April 2021
  • Revise Date: 23 January 2022
  • Accept Date: 29 January 2022
  • Published Online: 01 March 2023