144 research outputs found
Eccentric connectivity index
The eccentric connectivity index is a novel distance--based molecular
structure descriptor that was recently used for mathematical modeling of
biological activities of diverse nature. It is defined as \,, where and
denote the vertex degree and eccentricity of \,, respectively. We survey
some mathematical properties of this index and furthermore support the use of
eccentric connectivity index as topological structure descriptor. We present
the extremal trees and unicyclic graphs with maximum and minimum eccentric
connectivity index subject to the certain graph constraints. Sharp lower and
asymptotic upper bound for all graphs are given and various connections with
other important graph invariants are established. In addition, we present
explicit formulae for the values of eccentric connectivity index for several
families of composite graphs and designed a linear algorithm for calculating
the eccentric connectivity index of trees. Some open problems and related
indices for further study are also listed.Comment: 25 pages, 5 figure
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
Corrigendum on Wiener index, Zagreb Indices and Harary index of Eulerian graphs
In the original article ``Wiener index of Eulerian graphs'' [Discrete Applied
Mathematics Volume 162, 10 January 2014, Pages 247-250], the authors state that
the Wiener index (total distance) of an Eulerian graph is maximized by the
cycle. We explain that the initial proof contains a flaw and note that it is a
corollary of a result by Plesn\'ik, since an Eulerian graph is
-edge-connected. The same incorrect proof is used in two referencing papers,
``Zagreb Indices and Multiplicative Zagreb Indices of Eulerian Graphs'' [Bull.
Malays. Math. Sci. Soc. (2019) 42:67-78] and ``Harary index of Eulerian
graphs'' [J. Math. Chem., 59(5):1378-1394, 2021]. We give proofs of the main
results of those papers and the -edge-connected analogues.Comment: 5 Pages, 1 Figure Corrigendum of 3 papers, whose titles are combine
Some Topological Indices of Subgroup Graph of Symmetric Group
The concept of the topological index of a graph is increasingly diverse because researchers continue to introduce new concepts of topological indices. Researches on the topological indices of a graph which initially only examines graphs related to chemical structures begin to examine graphs in general. On the other hand, the concept of graphs obtained from an algebraic structure is also increasingly being introduced. Thus, studying the topological indices of a graph obtained from an algebraic structure such as a group is very interesting to do. One concept of graph obtained from a group is subgroup graph introduced by Anderson et al in 2012 and there is no research on the topology index of the subgroup graph of the symmetric group until now. This article examines several topological indices of the subgroup graphs of the symmetric group for trivial normal subgroups. This article focuses on determining the formulae of various Zagreb indices such as first and second Zagreb indices and co-indices, reduced second Zagreb index and first and second multiplicatively Zagreb indices and several eccentricity-based topological indices such as first and second Zagreb eccentricity indices, eccentric connectivity, connective eccentricity, eccentric distance sum and adjacent eccentric distance sum indices of these graphs
Spectral properties of geometric-arithmetic index
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. One of the main aims of algebraic graph theory is to determine how, or whether, properties of graphs are reflected in the algebraic properties of some matrices. The aim of this paper is to study the geometric-arithmetic index GA(1) from an algebraic viewpoint. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix that is a modification of the classical adjacency matrix involving the degrees of the vertices. Moreover, using this matrix, we define a GA Laplacian matrix which determines the geometric-arithmetic index of a graph and satisfies properties similar to the ones of the classical Laplacian matrix. (C) 2015 Elsevier Inc. All rights reserved.This research was supported in part by a Grant from Ministerio de Economía y Competitividad (MTM 2013-46374-P), Spain, and a Grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México
Leap Eccentric Connectivity Index of Subdivision Graphs
The second degree of a vertex in a simple graph is defined as the number of its second neighbors. The leap eccentric connectivity index of a graph M, L xi(c)(M), is the sum of the product of the second degree and the eccentricity of every vertex in M. In this paper, some lower and upper bounds of L xi(c)(S(M)) in terms of the numbers of vertices and edges, diameter, and the first Zagreb and third leap Zagreb indices are obtained. Also, the exact values of L xi(c)(S(M)) for some well-known graphs are computed
Bond Additive Modeling 1. Adriatic Indices
Some of the most famous molecular descriptors are bond additive, i.e. they are calculated as the
sum of edge contributions (Randić-type indices, Balaban-type indices, Wiener index and its modifications,
Szeged index...). In this paper, the methods of calculations of bond contributions of these descriptors are
analyzed. The general concepts are extracted, and based on these concepts a large class of molecular descriptors
is defined. These descriptors are named Adriatic indices.
An especially interesting subclass of these descriptors consists of 148 discrete Adriatic indices. They are
analyzed on the testing sets provided by the International Academy of Mathematical Chemistry, and it has
been shown that they have good predictive properties in many cases. They can be easily encoded in the
computer and it may be of interest to incorporate them in the existing software packages for chemical
modeling. It is possible that they could improve various QSAR and QSPR studies
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