Some New Results on Irregularity of Graphs

Tavakoli, Mostafa; Rahbarnia, Fereydon; Ашрафи, Али Реза

doi:10.14317/jami.2014.675

Cited by 21 publications

(11 citation statements)

References 13 publications

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“…There are several other papers concerning topological indices of different graph operations. For more results on topological indices of different graph operations, interested readers are referred to the papers [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Reformulated First Zagreb Index of Some Graph Operations

De¹,

Nayeem

Pal

2015

Mathematics

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“…In [6], Azari and Iranmanesh presented explicit formulas for computing the eccentric-distance sum of different graph operations. Interested readers are referred to [11,12,13,14,15,8,7,9] in this regard.…”

Section: Introductionmentioning

confidence: 99%

F-Index of some graph operations

De¹,

Nayeem

Pal

2016

Discrete Math. Algorithm. Appl.

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The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph.This was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced to study the structure-dependency of total π-electron energy. But this topological index was not further studied till then. Very recently, Furtula and Gutman [B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem., 53(4)(2015) 1184-1190.] reinvestigated the index and named it "forgotten topological index" or "F-index". In that paper, they present some basic properties of this index and showed that this index can enhance the physico-chemical applicability of Zagreb index.Here, we study the behavior of this index under several graph operations and apply our results to find the F-index of different chemically interesting molecular graphs and nano-structures.

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“…So, many chemical graphs can be generated by using simple graphs based on operations such as alkane (C 3 H 6 ) is the corona product of P 3 & N 2 , a type of cycloalkanes is cyclohexane (C 6 H 12 ) that is the corona product of C 6 & N 2 , a polynomial chain and nanotube (TUC 4 (m, n)) are the Cartesian product of P m & P 2 and C m & P 2 , and a fence and closed fence are the lexicographic product of P m & P 2 and C m & P 2 . Up till now, many results of the various TIs have been presented under different molecular graphs based on operations, see [26,[28][29][30][31][32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Zagreb Connection Indices of Molecular Graphs Based on Operations

et al. 2020

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Topological index (numeric number) is a mathematical coding of the molecular graphs that predicts the physicochemical, biological, toxicological, and structural properties of the chemical compounds that are directly associated with the molecular graphs. The Zagreb connection indices are one of the TIs of the molecular graphs depending upon the connection number (degree of vertices at distance two) appeared in 1972 to compute the total electron energy of the alternant hydrocarbons. But after that, for a long period, these are not studied by researchers. Recently, Ali and Trinajstic Mol. Inform. 372018,1−7 restudied the Zagreb connection indices and reported that the Zagreb connection indices comparatively to the classical Zagreb indices provide the better absolute value of the correlation coefficient for the thirteen physicochemical properties of the octane isomers (all these tested values have been taken from the website http://www.moleculardescriptors.eu). In this paper, we compute the general results in the form of exact formulae & upper bounds of the second Zagreb connection index and modified first Zagreb connection index for the resultant graphs which are obtained by applying operations of corona, Cartesian, and lexicographic product. At the end, some applications of the obtained results for particular chemical structures such as alkanes, cycloalkanes, linear polynomial chain, carbon nanotubes, fence, and closed fence are presented. In addition, a comparison between exact and computed values of the aforesaid Zagreb indices is also included.

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Some New Results on Irregularity of Graphs

Abstract: Suppose G is a simple graph. The irregularity of G, irr(G), is the summation of imb(e) over all edges uv = e ∈ G, where imb(e) = |deg(u) − deg(v)|. In this paper, we investigate the behavior of this graph parameter under some old and new graph operations.

Cited by 21 publications

References 13 publications

Reformulated First Zagreb Index of Some Graph Operations

Reformulated First Zagreb Index of Some Graph Operations

F-Index of some graph operations

Zagreb Connection Indices of Molecular Graphs Based on Operations

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