1,084 research outputs found
Extremal structures of graphs with given connectivity or number of pendant vertices
For a graph , the first multiplicative Zagreb index is the
product of squares of vertex degrees, and the second multiplicative Zagreb
index is the product of products of degrees of pairs of adjacent
vertices. In this paper, we explore graphs with extremal and
in terms of (edge) connectivity and pendant vertices. The
corresponding extremal graphs are characterized with given connectivity at most
and pendant vertices. In addition, the maximum and minimum values of
and are provided. Our results extend and enrich
some known conclusions.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0694
Simple Alcohols with the Lowest Normal Boiling Point Using Topological Indices
We find simple saturated alcohols with the given number of carbon atoms and
the minimal normal boiling point. The boiling point is predicted with a
weighted sum of the generalized first Zagreb index, the second Zagreb index,
the Wiener index for vertex-weighted graphs, and a simple index caring for the
degree of a carbon atom being incident to the hydroxyl group. To find extremal
alcohol molecules we characterize chemical trees of order , which minimize
the sum of the second Zagreb index and the generalized first Zagreb index, and
also build chemical trees, which minimize the Wiener index over all chemical
trees with given vertex weights.Comment: 22 pages, 5 figures, accepted in 2014 by MATCH Commun. Math. Comput.
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On the sharp lower bounds of Zagreb indices of graphs with given number of cut vertices
The first Zagreb index of a graph is the sum of the square of every
vertex degree, while the second Zagreb index is the sum of the product of
vertex degrees of each edge over all edges. In our work, we solve an open
question about Zagreb indices of graphs with given number of cut vertices. The
sharp lower bounds are obtained for these indices of graphs in
, where denotes the set of all -vertex
graphs with cut vertices and at least one cycle. As consequences, those
graphs with the smallest Zagreb indices are characterized.Comment: Accepted by Journal of Mathematical Analysis and Application
Efficient computation of trees with minimal atom-bond connectivity index
The {\em atom-bond connectivity (ABC) index} is one of the recently most
investigated degree-based molecular structure descriptors, that have
applications in chemistry. For a graph , the ABC index is defined as
, where is the
degree of vertex in and is the set of edges of . Despite many
attempts in the last few years, it is still an open problem to characterize
trees with minimal index. In this paper, we present an efficient approach
of computing trees with minimal ABC index, by considering the degree sequences
of trees and some known properties of the graphs with minimal index. The
obtained results disprove some existing conjectures end suggest new ones to be
set
On reformulated zagreb indices with respect to tricyclic graphs
The authors Milievi et al. introduced the reformulated
Zagreb indices, which is a generalization of classical Zagreb indices of
chemical graph theory. In the paper, we characterize the extremal properties of
the first reformulated Zagreb index. We first introduce some graph operations
which increase or decrease this index. Furthermore, we will determine the
extremal tricyclic graphs with minimum and maximum the first Zagreb index by
these graph operations.Comment: 8 pages,2 figure
Adapting the Interrelated Two-way Clustering method for Quantitative Structure-Activity Relationship (QSAR) Modeling of a Diverse Set of Chemical Compounds
Interrelated Two-way Clustering (ITC) is an unsupervised clustering method
developed to divide samples into two groups in gene expression data obtained
through microarrays, selecting important genes simultaneously in the process.
This has been found to be a better approach than conventional clustering
methods like K-means or self-organizing map for the scenarios when number of
samples much smaller than number of variables (n<<p). In this paper we used the
ITC approach for classification of a diverse set of 508 chemicals regarding
mutagenicity. A large number of topological indices (TIs), 3-dimensional, and
quantum chemical descriptors, as well as atom pairs (APs) have been used as
explanatory variables. In this paper, ITC has been used only for predictor
selection, after which ridge regression is employed to build the final
predictive model. The proper leave-one-out (LOO) method of cross-validation in
this scenario is to take as holdout each of the 508 compounds before predictor
thinning and compare the predicted values with the experimental data. ITC based
results obtained here are comparable to those developed earlier
Computing the Mostar index in networks with applications to molecular graphs
Recently, a bond-additive topological descriptor, named as the Mostar index,
has been introduced as a measure of peripherality in networks. For a connected
graph , the Mostar index is defined as , where for an edge we denote by the number of
vertices of that are closer to than to and by the number
of vertices of that are closer to than to . In this paper, we
generalize the definition of the Mostar index to weighted graphs and prove that
the Mostar index of a weighted graph can be computed in terms of Mostar indices
of weighted quotient graphs. As a consequence, we show that the Mostar index of
a benzenoid system can be computed in sub-linear time with respect to the
number of vertices. Finally, our method is applied to some benzenoid systems
and to a fullerene patch
Topological indices of k-th subdivision and semi total point graphs
Graph theory has provided a very useful tool, called topological indices
which are a number obtained from the graph with the property that every
graph isomorphic to , value of a topological index must be same for both
and . In this article, we present exact expressions for some topological
indices of k-th subdivision graph and semi total point graphs respectively,
which are a generalization of ordinary subdivision and semi total graph for
.Comment: 14 page
Computing weighted Szeged and PI indices from quotient graphs
The weighted Szeged index and the weighted vertex-PI index of a connected
graph are defined as and , respectively, where denotes the number of vertices
closer to than to and denotes the number of vertices closer to
than to . Moreover, the weighted edge-Szeged index and the weighted PI
index are defined analogously. As the main result of this paper, we prove that
if is a connected graph, then all these indices can be computed in terms of
the corresponding indices of weighted quotient graphs with respect to a
partition of the edge set that is coarser than the -partition. If
is a benzenoid system or a phenylene, then it is possible to choose a partition
of the edge set in such a way that the quotient graphs are trees. As a
consequence, it is shown that for a benzenoid system the mentioned indices can
be computed in sub-linear time with respect to the number of vertices.
Moreover, closed formulas for linear phenylenes are also deduced. However, our
main theorem is proved in a more general form and therefore, we present how it
can be used to compute some other topological indices
Further results on degree based topological indices of certain chemical networks
There are various topological indices such as degree based topological
indices, distance based topological indices and counting related topological
indices etc. These topological indices correlate certain physicochemical
properties such as boiling point, stability of chemical compounds. In this
paper, we compute the sum-connectivity index and multiplicative Zagreb indices
for certain networks of chemical importance like silicate networks, hexagonal
networks, oxide networks, and honeycomb networks. Moreover, a comparative study
using computer-based graphs has been made to clarify their nature for these
families of networks.Comment: Submitte
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