Can topological indices transmit information on properties but not on structures?

Balaban, Alexandrù T.

doi:10.1007/s10822-005-9010-6

Cited by 23 publications

(16 citation statements)

References 63 publications

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“…There are number of topological indices of high discriminatory power 55–62. Hence, of indices of high discriminatory power, there is a lack of such indices having straightforward structural interpretation, because most of such descriptors involve various arbitrary constructional elements, and in addition, some involve conceptual or computational complexity.…”

Section: More On Properties Of Natural Distance Matricesmentioning

confidence: 99%

Novel graph distance matrix

et al. 2010

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We have introduced novel distance matrix for graphs, which is based on interpretation of columns of the adjacency matrix of a graph as a set of points in n-dimensional space, n being the number of vertices in the graph. Numerical values for the distances are based on the Euclidean distance between n points in n-dimensional space. In this way, we have combined the traditional representation of graphs (drawn as 2D object of no fixed geometry) with their representation in n-dimensional space, defined by a set of n-points that lead to a representation of definite geometry. The novel distance matrix, referred to as natural distance matrix, shows some structural properties and offers novel graph invariants as molecular descriptors for structure-property-activity studies. One of the novel graph descriptors is the modified connectivity index in which the bond contribution for (m, n) bond-type is given by 1/ radical(m + n), where m and n are the valence of the end vertices of the bond. The novel distance matrix (ND) can be reduced to sparse distance-adjacency matrix (DA), which can be viewed as specially weighted adjacency matrix of a graph. The quotient of the leading eigenvalues of novel distance-adjacency matrix and novel distance matrix, as illustrated on a collection of graphs of chemical interest, show parallelism with a simple measure of graph density, based on the quotient of the number of edges in a graph and the maximal possible number of edges for graphs of the same size.

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Section: More On Properties Of Natural Distance Matricesmentioning

confidence: 99%

Novel graph distance matrix

et al. 2010

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“…Recently, an inverse problem based on the k -th Steiner Wiener index (a generalized version of Wiener index) was studied in the paper [ 36 ]. Further details about inverse problem can be found in the survey [ 37 ], recent papers [ 38 , 39 ] and related references listed therein.…”

Section: Introductionmentioning

confidence: 99%

The inverse Wiener polarity index problem for chemical trees

Ali

2018

PLoS ONE

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The Wiener polarity number (which, nowadays, known as the Wiener polarity index and usually denoted by Wp) was devised by the chemist Harold Wiener, for predicting the boiling points of alkanes. The index Wp of chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices (carbon atoms) at distance 3. The inverse problems based on some well-known topological indices have already been addressed in the literature. The solution of such inverse problems may be helpful in speeding up the discovery of lead compounds having the desired properties. This paper is devoted to solving a stronger version of the inverse problem based on Wiener polarity index for chemical trees. More precisely, it is proved that for every integer t ∈ {n − 3, n − 2,…,3n − 16, 3n − 15}, n ≥ 6, there exists an n-vertex chemical tree T such that Wp(T) = t.

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“…A recent trend in theoretical chemistry is the use of topological indices in predicting the certain properties of chemical compounds. [1][2][3][4] The first Zagreb index , occurred in an approximate formula of total π-electron energy, 5 and the second Zagreb index , appeared within the study of molecular branching, 6 are among the most studied topological indices. These topological index are defined as…”

Section: Introductionmentioning

confidence: 99%

Zagreb Connection Indices of Some Nanostructures

et al. 2018

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The first Zagreb index (occurred in an approximate formula of total π-electron energy, communicated in 1972) and the second Zagreb index (appeared in 1975, within the study of molecular branching) are among the most studied topological indices. Recently, three modified versions of the Zagreb indices were proposed independently in [A. Ali, N. Trinajstić, A novel/old modification of the first Zagreb index, arXiv:1705.10430 [math.CO], 2017] and [A. M. Naji, N. D. Soner, I. Gutman, On leap Zagreb indices of graphs, Commun. Comb. Optim., 2017, 2, 99–117], which were named as the Zagreb connection indices and the leap Zagreb indices, respectively. In this paper, we derive formulas for calculating these modified versions of the Zagreb indices of four well known nanostructures.

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Can topological indices transmit information on properties but not on structures?

Cited by 23 publications

References 63 publications

Novel graph distance matrix

Novel graph distance matrix

The inverse Wiener polarity index problem for chemical trees

Zagreb Connection Indices of Some Nanostructures

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