Calculating the edge Wiener and edge Szeged indices of graphs

Yousefi-Azari, H.; Khalifeh, M. H.; Ashrafi, Ali Reza

doi:10.1016/j.cam.2011.02.019

Cited by 51 publications

(22 citation statements)

References 13 publications

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“…The authors apparently missed the whole series of papers that deal with computing distance based indices using the cut method. The same method was successively applied to hyper Wiener index [1], Szeged index [6], PI index [15], the edge-Wiener and edge-Szeged index [18], degree distance [7], weighted Wiener index [17], terminal Wiener index [8], etc. For some other applications and properties see [3], [4], [12], [13].…”

Section: Cut Methodsmentioning

confidence: 99%

A Note on 'A New Approach to Compute Wiener Index'

Ilić¹

2014

j comput theor nanosci

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In this note, we discuss the method explained in the recent paper [P. Manuel, I. Rajasingh, B. Rajan, R. Sundara Rajan, A New Approach To Compute Wiener Index, Journal of Computational and Theoretical Nanoscience 10, (2013) 1515-1521.] for computing the Wiener index of special chemical graphs. The method is actually already well-known and equivalent to the 'cut method' introduced in 1995 by Klavžar, Gutman and Mohar, and used in multiple papers for computing various distance based graph invariants.

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Section: Cut Methodsmentioning

confidence: 99%

A Note on 'A New Approach to Compute Wiener Index'

Ilić¹

2014

j comput theor nanosci

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“…Corollary Let G be the circumcorone series benzenoid system H k , k ⩾ 1. W ( G ) = k (164 k 4 − 30 k 2 + 1)/5, W e ( G ) = 3 k (246 k 4 − 340 k 3 + 140 k 2 − 5 k − 1)/10, W e v ( G ) = k (492 k 4 − 340 k 3 + 25 k + 3)/10, S z v ( G ) = 3 k 2 (36 k 4 − k 2 + 1)/2, S z e ( G ) = k (1215 k 5 − 1599 k 4 + 680 k 3 − 105 k 2 + 55 k − 6)/10, S z e v ( G ) = k (1620 k 5 − 1066 k 4 + 135 k 3 − 10 k 2 + 45 k − 4)/20, S z t ( G ) = k (675 k 5 − 533 k 4 + 160 k 3 − 23 k 2 + 23 k − 2)/2, P I ( G ) = 81 k 4 − 68 k 3 + 12 k 2 − k , S ( G ) = 2 k (492 k 4 − 205 k 3 − 45 k 2 + 25 k + 3)/5, G u t ( G ) = k (1476 k 4 − 1230 k 3 + 230 k 2 + 75 k − 11)/5. …”

Section: Distance‐based Topological Indicesmentioning

confidence: 99%

Analytical expressions for topological properties of polycyclic benzenoid networks

Arockiaraj¹,

Clement²,

Balasubramanian

2016

Journal of Chemometrics

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Quantitative structure-activity and structure-property relationships of complex polycyclic benzenoid networks require expressions for the topological properties of these networks. Structure-based topological indices of these networks enable prediction of chemical properties and the bioactivities of these compounds through quantitative structure-activity and structure-property relationships methods. We consider a number of infinite convex benzenoid networks that include polyacene, parallelogram, trapezium, triangular, bitrapezium, and circumcorone series benzenoid networks. For all such networks, we compute analytical expressions for both vertex-degree and edge-based topological indices such as edge-Wiener, vertex-edge Wiener, vertex-Szeged, edge-Szeged, edge-vertex Szeged, total-Szeged, Padmakar-Ivan, Schultz, Gutman, Randić, generalized Randić, reciprocal Randić, reduced reciprocal Randić, first Zagreb, second Zagreb, reduced second Zagreb, hyper Zagreb, augmented Zagreb, atom-bond connectivity, harmonic, sum-connectivity, and geometric-arithmetic indices. In addition we have obtained expressions for these topological indices for 3 types of parallelogram-like polycyclic benzenoid networks. KEYWORDSconvex polycyclic benzenoid networks, cut method, QSAR of polycyclic aromatics, topological indices 1 682

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“…Graph invariants constitute an interesting tool in Chemistry, Communication or Engineering [8,16,19]. In Mathematics, one of the topics for which graph invariants have revealed to play an important role is the classical problem of deciding whether two algebras are isomorphic.…”

Section: Introductionmentioning

confidence: 99%

Computation of isotopisms of algebras over finite fields by means of graph invariants

Falcón

Ganfornina

Núñez

et al. 2017

Journal of Computational and Applied Mathematics

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In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine whether two algebras are isomorphic. In order to illustrate their efficiency, we determine explicitly the classification of two-and threedimensional partial quasigroup rings.

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Calculating the edge Wiener and edge Szeged indices of graphs

Cited by 51 publications

References 13 publications

A Note on 'A New Approach to Compute Wiener Index'

A Note on 'A New Approach to Compute Wiener Index'

Analytical expressions for topological properties of polycyclic benzenoid networks

Computation of isotopisms of algebras over finite fields by means of graph invariants

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