scholarly journals A graph theoretical approach to cis/trans isomerism

2014 ◽  
Vol 79 (7) ◽  
pp. 805-813 ◽  
Author(s):  
Boris Furtula ◽  
Giorgi Lekishvili ◽  
Ivan Gutman
Keyword(s):  
Graph Theory ◽  
Electron Energy ◽  
Theoretical Approach ◽  
Adjacency Matrix ◽  
Molecular Graph ◽  
Energy Difference ◽  
Simple Graph ◽  
Total Electron ◽  
Total Electron Energy ◽  
Graph Theoretical Approach

A simple graph-theory-based model is put forward, by means of which it is possible to express the energy difference between geometrically non-equivalent forms of a conjugated polyene. This is achieved by modifying the adjacency matrix of the molecular graph, and including into it information on cis/trans constellations. The total ?-electron energy thus calculated is in excellent agreement with the enthalpies of the underlying isomers and conformers.

scholarly journals Total π-electron energy and Laplacian energy: How far the analogy goes?

2007 ◽  
Vol 72 (12) ◽  
pp. 1343-1350 ◽  
Author(s):  
Slavko Radenkovic ◽  
Ivan Gutman
Keyword(s):  
Electron Energy ◽  
Linear Correlation ◽  
Molecular Graph ◽  
Total Electron ◽  
Good Linear ◽  
Molecular Graphs ◽  
Acyclic Graphs ◽  
Laplacian Energy ◽  
Total Electron Energy ◽  
Good Linear Correlation

The Laplacian energy LE is a newly introduced molecular-graph-based analog of the total ?-electron energy E. It is shown that LE and E have a similar structure-dependency only when molecules of different sizes are compared, when a good linear correlation between them exists. Within classes of isomers, LE and E are either not correlated at all or (as in the case of acyclic systems) are inversely proportional. The acyclic graphs and molecular graphs having the greatest and smallest LE values (determined in this work) differ significantly from those (previously known) having the greatest and smallest E values.

scholarly journals Dependence of the total -electron energy on large number of non-bonding molecular orbitals

2004 ◽  
Vol 69 (10) ◽  
pp. 777-782 ◽  
Author(s):  
Ivan Gutman ◽  
Dragan Stevanovic ◽  
Slavko Radenkovic ◽  
Svetlana Milosavljevic ◽  
Natasa Cmiljanovic
Keyword(s):  
Electron Energy ◽  
Molecular Orbitals ◽  
Total Electron ◽  
Total Electron Energy

Using a recently developed method for computing the effect of non-bonding molecular orbitals (NBMOs) on the total ?-electron energy (E), it was found that the dependence of E on the number n0 of NBMOs is almost perfectly linear. We now show that this regularity remains valid for very large values of n0, in particular, to hold up to n0 = 20.

scholarly journals Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yajing Wang ◽  
Yubin Gao
Keyword(s):  
Graph Theory ◽  
Spectral Radius ◽  
Adjacency Matrix ◽  
Upper Bounds ◽  
Simple Graph ◽  
Spectral Graph Theory ◽  
Extremal Graphs ◽  
Spectral Graph ◽  
Vertex Set

Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

A topological index for the total?-electron energy

1975 ◽  
Vol 38 (1) ◽  
pp. 37-47 ◽  
Author(s):  
Haruo Hosoya ◽  
Kikuko Hosoi ◽  
Ivan Gutman
Keyword(s):  
Electron Energy ◽  
Topological Index ◽  
Total Electron ◽  
Total Electron Energy

scholarly journals Tripartite graphs with energy aggregation

2019 ◽  
Vol 38 (7) ◽  
pp. 149-167 ◽  
Author(s):  
Nawras A. Alawn ◽  
Nadia M. G. Al-Saidi ◽  
Rashed T. Rasheed
Keyword(s):  
Electron Energy ◽  
Degree Sequence ◽  
Maximum Energy ◽  
Chemical Components ◽  
Research Attention ◽  
Total Electron ◽  
Tripartite Graph ◽  
Total Electron Energy ◽  
Irregular Graphs ◽  
Tripartite Graphs

The aggregate of the absolute values of the graph eigenvalues is called the energy of a graph. It is used to approximate the total _-electron energy of molecules. Thus, finding a new mechanism to calculate the total energy of some graphs is a challenge; it has received a lot of research attention. We study the eigenvalues of a complete tripartite graph Ti,i,n−2i , for n _ 4, based on the adjacency, Laplacian, and signless Laplacian matrices. In terms of the degree sequence, the extreme eigenvalues of the irregular graphs energy are found to characterize the component with the maximum energy. The chemical HMO approach is particularly successful in the case of the total _-electron energy. We showed that some chemical components are equienergetic with the tripartite graph. This discovering helps easily to derive the HMO for most of these components despite their different structures.

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