Reminescences

Modified Zagreb M₂ Index – Comparison with the Randić Connectivity Index for Benzenoid Systems

Damir Vukičević ; Department of Mathematics, University of Split, HR-21000 Split, Croatia
Nenad Trinajstić ; The Rugjer Bošković Institute, P. O. Box 180, HR-10002 Zagreb, Croatia

Abstract

Two theorems have been derived for benzenoid systems with the following implications: (i) for any arbitrarily large m (e.g., m = 1000000) there is a number n and a set with m benzenoid systems with n vertices so that every pair of them posseses the same Randić connectivity index, but no two graphs exist with the same modified Zagreb M₂ index, and (ii) for any arbitrarily large m (e.g., m = 10000000) there is a number n and a set with m benzenoid systems with n vertices so that (a) every pair of graphs posseses a different Randić connectivity index, (b) every pair of graphs has a different modified Zagreb M₂ index, and (c) Randić connectivity indices order these graphs in the reverse order with respect to modified Zagreb M₂ indices. We have shown with these two theorems that the modified Zagreb M₂ index differs fundamentally from the Randić connectivity index.

Keywords

benzenoid systems; modified Zagreb M₂ index; Randić connectivity index

Hrčak ID:

103095

URI

https://hrcak.srce.hr/103095

Publication date:

30.6.2003.

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