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Fatemeh Koorepazan-Moftakhar (University of Kashan, Iran), Ali Reza Ashrafi (University of Kashan, Iran), Ottorino Ori (Actinium Chemical Research, Italy & West University of Timişoara, Romania) and Mihai V. Putz (West University of Timişoara, Romania & Research and Development National Institute for Electrochemistry and Condensed Matter (INCEMC) Timişoara, Romania)

Copyright: © 2017
|Pages: 42

DOI: 10.4018/978-1-5225-0492-4.ch017

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Top*Mathematical chemistry* is concerned with the application of mathematical and computational techniques in chemistry, but it should not be confused with *computational chemistry*. Major areas of research in mathematical chemistry include *chemical graph theory*. This branch of mathematical chemistry is dealing with the topological description of molecules as well as the mathematical modeling of chemical phenomena. This part of mathematical chemistry is used to model physical properties of molecules. To do this, some structural numbers named *topological indices* based on the graphical structure of molecules are defined. The main problem of molecular graph theory is ability of these models and their errors. In our study, we will consider simple molecular graphs without loops and multiple edges.

In chemical graph theory, two different sets of objects are usually considered: *atoms* and *chemical bonds*. Define *V* and *E* as the set of all atoms and chemical bonds. Then the pair G = (V,E) has a topological structure named “molecular graph”. A chemical bond *e* connects two atoms *u* and *v* and it is convenient to write *e = uv*. We also use the terms *vertex* and *edge* for atom and chemical bond, respectively. The *degree* of a vertex *v, deg _{G}*(

If *G* and *H* are graphs, V(H) ⊆ V(G) and E(H) ⊆ E(G) then H is called a *subgraph* of G written as *H* ≤ *G*. A *path P* in a molecular graph *G* is a subgraph with the property that *V*(*P*) = {*v _{1}, v_{2}, …, v_{n}*} and

A fullerene is a carbon sphere−like molecule such that its molecular graph is planar, cubic, 3−connected and all faces are pentagon or hexagon. By Euler’s Theorem, it is easy to prove that the number of pentagons and hexagons in an n−vertex fullerene is 12 and n/2 – 10, respectively. The study of these molecular graphs started after the discovery of buckminsterfullerene by Kroto *et al.* (Kroto et al., 1985).

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