Sharp upper bounds for total π-electron energy of alternant hydrocarbons

2007 ◽  
Vol 43 (2) ◽  
pp. 713-718 ◽  
Author(s):  
Ji-Ming Guo
Keyword(s):  
Electron Energy ◽  
Upper Bounds ◽  
Alternant Hydrocarbons

scholarly journals Computing Analysis for First Zagreb Connection Index and Coindex of Resultant Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-19 ◽  
Author(s):  
Muhammad Javaid ◽  
Usman Ali ◽  
Jia-Bao Liu
Keyword(s):  
Tensor Product ◽  
Physicochemical Properties ◽  
Electron Energy ◽  
Topological Index ◽  
Chemical Compounds ◽  
Upper Bounds ◽  
Symmetric Difference ◽  
Factor Graphs ◽  
Strong Product ◽  
Alternant Hydrocarbons

A numeric parameter which studies the behaviour, structural, toxicological, experimental, and physicochemical properties of chemical compounds under several graphs’ isomorphism is known as topological index. In 2018, Ali and Trinajstić studied the first Zagreb connection index Z C 1 to evaluate the value of a molecule. This concept was first studied by Gutman and Trinajstić in 1972 to find the solution of π -electron energy of alternant hydrocarbons. In this paper, the first Zagreb connection index and coindex are obtained in the form of exact formulae and upper bounds for the resultant graphs in terms of different indices of their factor graphs, where the resultant graphs are obtained by the product-related operations on graphs such as tensor product, strong product, symmetric difference, and disjunction. At the end, an analysis of the obtained results for the first Zagreb connection index and coindex on the aforesaid resultant graphs is interpreted with the help of numerical values and graphical depictions.

scholarly journals Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1320
Author(s):  
Usman Ali ◽  
Muhammad Javaid ◽  
Abdulaziz Mohammed Alanazi
Keyword(s):  
Carbon Nanotube ◽  
Electron Energy ◽  
Upper Bounds ◽  
Molecular Networks ◽  
Connection Number ◽  
Zagreb Indices ◽  
Linear Polynomial ◽  
Degree Of A Vertex ◽  
Octane Isomers ◽  
Alternant Hydrocarbons

Gutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the isomorphic (molecular) networks. For the prediction of physicochemical and symmetrical properties of octane isomers, these indices are restudied in 2018. In this paper, first and second Zagreb connection coindices are defined and obtained in the form of upper bounds for the resultant networks in the terms of different indices of their factor networks, where resultant networks are obtained from two networks by the product-related operations, such as cartesian, corona, and lexicographic. For the molecular networks linear polynomial chain, carbon nanotube, alkane, cycloalkane, fence, and closed fence, first and second Zagreb connection coindices are computed in the consequence of the obtained results. An analysis of Zagreb connection indices and coindices on the aforesaid molecular networks is also included with the help of their numerical values and graphical presentations that shows the symmetric behaviour of these indices and coindices with in certain intervals of order and size of the under study (molecular) networks.

scholarly journals Estimating and Approximating the Total π-Electron Energy of Benzenoid Hydrocarbons

2000 ◽  
Vol 55 (5) ◽  
pp. 507-512 ◽  
Author(s):  
I. Gutman ◽  
J. H. Koolen ◽  
V. Moulto ◽  
M. Parac ◽  
T. Soldatović ◽  
...  
Keyword(s):  
Electron Energy ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Benzenoid Hydrocarbons ◽  
Carbon Carbon Bonds ◽  
Carbon Bonds ◽  
Approximate Formulas ◽  
Better Than

Abstract Lower and upper bounds as well as approximate formulas for the total π-electron energy (E) of benzenoid hydrocarbons are deduced, depending only on the number of carbon atoms (n) and number of carbon-carbon bonds (to). These are better than the several previously known (n, m)-type estimates and approximations for E.

Generalizing the McClelland Bounds for Total π-Electron Energy

2008 ◽  
Vol 63 (5-6) ◽  
pp. 280-282 ◽  
Author(s):  
Ivan Gutman ◽  
Gopalapillai Indulal ◽  
Roberto Todeschinic
Keyword(s):  
Electron Energy ◽  
Distance Matrix ◽  
Upper Bounds ◽  
Arithmetic Mean ◽  
Lower And Upper Bounds ◽  
Real Numbers ◽  
Laplacian Energy ◽  
Graph Energy

In 1971 McClelland obtained lower and upper bounds for the total π-electron energy. We now formulate the generalized version of these bounds, applicable to the energy-like expression EX = Σni =1 |xi − x̅|, where x1,x2, . . . ,xn are any real numbers, and x̅ is their arithmetic mean. In particular, if x1,x2, . . . ,xn are the eigenvalues of the adjacency, Laplacian, or distance matrix of some graph G, then EX is the graph energy, Laplacian energy, or distance energy, respectively, of G.

scholarly journals Iterative estimation of total π-electron energy

2005 ◽  
Vol 70 (10) ◽  
pp. 1193-1197 ◽  
Author(s):  
Lemi Türker ◽  
Ivan Gutman
Keyword(s):  
Lower Bound ◽  
Electron Energy ◽  
Upper Bound ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Benzenoid Hydrocarbons ◽  
Total Electron ◽  
Iterative Estimation ◽  
Total Electron Energy ◽  
Almost All

In this work, the lower and upper bounds for total ?-electron energy (E) was studied. A method is presented, by means of which, starting with a lower bound EL and an upper bound EU for E, a sequence of auxiliary quantities E0 E1, E2,? is computed, such that E0 = EL, E0 < E1 < E2 < ?, and E = EU. Therefore, an integer k exists, such that Ek E < Ek+1. If the estimates EL and EU are of the McClelland type, then k is called the McClelland number. For almost all benzenoid hydrocarbons, k = 3.

Total π-Electron Energy of Conjugated Molecules with Non-bonding Molecular Orbitals

2016 ◽  
Vol 71 (2) ◽  
pp. 161-164 ◽  
Author(s):  
Ivan Gutman
Keyword(s):  
Electron Energy ◽  
Upper Bounds ◽  
Molecular Orbitals ◽  
Electron Systems ◽  
Lower And Upper Bounds ◽  
Conjugated Molecules

AbstractLower and upper bounds for the totalπ-electron energy are obtained, which are applicable to conjugatedπ-electron systems with non-bonding molecular orbitals (NBMOs). These improve the earlier estimates, in which the number of NBMOs has not been taken into account.

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