33,364 research outputs found
Bounds on the arithmetic-geometric index
The concept of arithmetic-geometric index was recently introduced in chemical graph theory, but it has proven to be useful from both a theoretical and practical point of view. The aim of this paper is to obtain new bounds of the arithmetic-geometric index and characterize the extremal graphs with respect to them. Several bounds are based on other indices, such as the second variable Zagreb index or the general atom-bond connectivity index), and some of them involve some parameters, such as the number of edges, the maximum degree, or the minimum degree of the graph. In most bounds, the graphs for which equality is attained are regular or biregular, or star graphs.This research was supported by a grant from Agencia Estatal de Investigación (PID2019-106433GBI00/ AEI/10.13039/501100011033), Spain. The research of José M. RodrÃguez was supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)
On the distance spectrum and distance-based topological indices of central vertex-edge join of three graphs
Topological indices are molecular descriptors that describe the properties of
chemical compounds. These topological indices correlate specific
physico-chemical properties like boiling point, enthalpy of vaporization,
strain energy, and stability of chemical compounds. This article introduces a
new graph operation based on central graph called central vertex-edge join and
provides its results related to graph invariants like eccentric-connectivity
index, connective eccentricity index, total-eccentricity index, average
eccentricity index, Zagreb eccentricity indices, eccentric geometric-arithmetic
index, eccentric atom-bond connectivity index, and Wiener index. Also, we
discuss the distance spectrum of the central vertex-edge join of three regular
graphs. Furthermore, we obtain new families of -equienergetic graphs, which
are non -cospectral
Computing Some Degree-Based Topological Indices of Graphene
Graphene is one of the most promising nanomaterial because of its unique combination of superb properties, which opens a way for its exploitation in a wide spectrum of applications ranging from electronics to optics, sensors, and bio devices. Inspired by recent work on Graphene of computing topological indices, here we compute new topological indices viz. Arithmetic-Geometric index (AG2 index), SK3 index and Sanskruti index of a molecular graph G and obtain the explicit formulae of these indices for Graphene
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
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