26,199 research outputs found
More on Comparison Between First Geometric-Arithmetic Index and Atom-Bond Connectivity Index
The first geometric-arithmetic (GA) index and atom-bond connectivity (ABC)
index are molecular structure descriptors which play a significant role in
quantitative structure-property relationship (QSPR) and quantitative
structure-activity relationship (QSAR) studies. Das and Trinajsti\'{c}
[\textit{Chem. Phys. Lett.} \textbf{497} (2010) 149-151] showed that index
is greater than index for all those graphs (except and ,
see Figure 1) in which the difference between maximum and minimum degree is
less than or equal to 3. In this note, it is proved that index is greater
than index for line graphs of molecular graphs, for general graphs in
which the difference between maximum and minimum degree is less than or equal
to (where is the minimum degree and )
and for some families of trees. Thereby, a partial solution to an open problem
proposed by Das and Trinajsti\'{c} is given.Comment: 10 pages, 2 tables, 1 figure, revised versio
Quasi-isometric classification of non-geometric 3-manifold groups
We describe the quasi-isometric classification of fundamental groups of
irreducible non-geometric 3-manifolds which do not have "too many" arithmetic
hyperbolic geometric components, thus completing the quasi-isometric
classification of 3--manifold groups in all but a few exceptional cases.Comment: Minor revision (added footnote in the Introduction
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