Izvorni znanstveni članak

https://doi.org/10.5562/cca1579

On a Relation Between the Zagreb Indices

Sanja Stevanović orcid.org/0000-0001-7723-3417 ; University of Niš, Faculty of Civil Engineering and Architecture, Aleksandra Medvedeva bb, 18000 Niš, Serbia

Sažetak

Let G=(V,E) be a simple graph with n=|V| vertices and m=|E| edges. The first and the second Zagreb index are defined as M1=∑u∈Vdu2 and M2=∑uv∈Edudv, where du is the degree of vertex u. Professor Pierre Hansen at the International Academy of Mathematical Chemistry Meeting in 2006 conjectured that 1Mm≤2Mnholds for all simple graphs. While the conjecture is true for trees, unicyclic and chemical graphs, several counterexamples appeared in the literature. Here we extend the construction of counterexamples by showing that we may add a sufficiently large star to any graph G with m≥n+δ to obtain a counterexample. For the variable Zagreb indices λM1=∑u∈Vdu2λ and λM2=∑uv∈Eduλdvλ, we prove that any graph G can be extended by a suitably large star so that λM1/n>λM2/m when 0<λ<1, and λM1/n<λM2/m when λ<0 or λ>1. (doi: 10.5562/cca1579)

Ključne riječi

molecular structure descriptor; Zagreb indices

Hrčak ID:

69689

URI

https://hrcak.srce.hr/69689

Datum izdavanja:

30.5.2011.

Posjeta: 2.497 *