Estrada Index of Benzenoid Hydrocarbons

Abstract

A structure-descriptor EE, recently proposed by Estrada, is examined. If λ 1 , λ 2 ,...,λ n are the eigenvalues of the molecular graph, then EE = n ∑ i=1 e λ i . In the case of benzenoid hydrocarbons with n carbon atoms and m carbon-carbon bonds, EE is found to be accurately approximated by means of the formula a 1 n cosh 2m/n + a 2 , where a 1 ≈ 1.098 and a 2 = −0.64 are empirically determined fitting constants. Within classes of benzenoid isomers (which all have equal n and m), the Estrada index is linearly proportional to the number of bay regions.

The many facets of the Estrada indices of graphs and networks

“…3, where the lower bound is always drawn in blue and the upper one in red. The means and standard deviations of the General [10,38,63,101,121,189,198,201,238] Weighted general [197,200] Trees [55,62,159,188,244] Molecular trees [115,134] Unicyclic [64] Bicyclic [228] Tricyclic [252] Tetracyclic [186] Pentacyclic [185] Bipartite [91,120,245,250] Line graphs [4,208] Strongly quotients [33] Folded hypercubes [165] Cacti [157] Cayley [103] Specific graphs [104] Ramanujan [199] Benzenoids [118] Phenylenes [187] Fullerenes [14] Möbius [96] lower, upper bounds are as follow: Bound In Fig. 4 we illustrate the results for the five real-world networks considered in this work.…”

Spectral Properties of Fullerenes

“…12 Some mathematical properties of the Estrada index and its basic computational techniques were reported in Refs. [13][14][15][16][17][18][19][20][21][22][23].…”

Alkanes with Greatest Estrada Index

“…Details on its theory and applications can be found in recent articles [19,20] as well as in Ernesto Estrada's original papers [21 -26]. It is defined as follows:…”