Authors: Milošević, Marko
Réti, Tamás
Stevanović, Dragan 
Title: On the constant difference of Zagreb Indices
Journal: Match
Volume: 68
Issue: 1
First page: 157
Last page: 168
Issue Date: 1-Dec-2012
Rank: M21a
ISSN: 0340-6253
Let Φ(z), z ∈ ℤ, be the set of all connected graphs whose difference of the second and the first Zagreb index is equal to z. We show that Φ(z) contains exactly one element, a star, for z < -2, while it is infinite for z ≥ -2. Moreover, all elements of Φ(-2) and Φ(-1) are trees, while Φ(0), besides trees, contains the cycles only Constructions of new elements of Φ(z) from the existing ones are based on the existence of vertices of degree two. We further show that the only elements of J z≤0Φ(z), which do not contain vertices of degree two, are stars and the molecular graphs of 2,3-dimethylbutane and 2,2,3-trimethylbutane.
Publisher: Faculty of Sciences, University of Kragujevac
Project: Graph theory and mathematical programming with applications in chemistry and computer science 
Slovenian Research Agency, research grants P1-0285 and J1-4021

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