The first and second Zagreb indices of some graph operations

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

doi:10.1016/j.dam.2008.06.015

Cited by 219 publications

(134 citation statements)

References 13 publications

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“…The splice of two graphs G 1 and G 2 at the vertices y and z is denoted by (G 1 • G 2 )(y, z) and is obtained by identifying the vertices y and z in the union of G 1 and G 2 . The vertex set of ( 12 , where we denote the vertex obtained by identifying y and z by v 12 . From the construction of the splice of two graphs it is clear that…”

Section: Splice Of Graphsmentioning

confidence: 99%

“…Graph operations play a very important role in mathematical chemistry, since some chemically interesting graphs can be obtained from some simpler graphs by different graph operations. In [12], Khalifeh et al, derived some exact expressions for computing first and second Zagreb indices of some graph operations. Ashrafi et al [13] derived explicit expressions for Zagreb coindices of different graph operations.…”

Section: Introductionmentioning

confidence: 99%

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Reformulated First Zagreb Index of Some Graph Operations

De¹,

Nayeem

Pal

2015

Mathematics

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Abstract:The reformulated Zagreb indices of a graph are obtained from the classical Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of the end vertices of the edge minus 2. In this paper, we study the behavior of the reformulated first Zagreb index and apply our results to different chemically interesting molecular graphs and nano-structures.

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Section: Splice Of Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reformulated First Zagreb Index of Some Graph Operations

De¹,

Nayeem

Pal

2015

Mathematics

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“…In [14], Klavžar, Rajapakse and Gutman computed the Szeged index of the Cartesian product graphs. The present authors, [8,9,10,11,12,13,22], computed some exact formulae for the hyper-Wiener, vertex PI, edge PI, the first Zagreb, the second Zagreb, the edge Wiener and the edge Szeged indices of some graph operations. The aim of this section is to continue this program for computing the Wiener-type invariants for five graph operations.…”

Section: Resultsmentioning

confidence: 99%

Wiener-type invariants of some graph operations

Hossein-Zadeh

Hamzeh

Ашрафи

2009

Filomat

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Let d (G, k) be the number of pairs of vertices of a graph G that are at distance k, λ a real number, andis called the Wiener-type invariant of G associated to real number λ. In this paper, the Wiener-type invariants of some graph operations are computed. As immediate consequences, the formulae for reciprocal Wiener index, Harary index, hyperWiener index and Tratch-Stankevich-Zefirov index are calculated. Some upper and lower bounds are also presented.

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“…In [17], Klavžar, Rajapakse and Gutman computed the Szeged index of the Cartesian product graphs. The recent authors, [1,2,9,11,12,13,14,15,16,18,24], computed some exact formulas for the hyper-Wiener, vertex PI, edge PI, the first Zagreb, the second Zagreb, the edge Wiener and the edge Szeged indices of some graph operations. The aim of this section is to continue this program for computing the GA 2 index of these graph operations.…”

Section: Resultsmentioning

confidence: 99%