ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...

Large carbon molecules, discovered at the end of the last century, are called fullerenes. The most famous of these, C60 has the structure of the soccer ball: the seams represent chemical bonds and the points where three seams come together represent the carbon atoms. We use the term fullerene to represent all mathematically possible structures for the chemical fullerenes: trivalent plane graphs...

S of the Ghent Graph Theory Workshop on Longest Paths and Longest Cycles Kathie Cameron Degree-constrained spanning trees 2 Jan Goedgebeur Finding minimal obstructions to graph coloring 3 Jochen Harant On longest cycles in essentially 4-connected planar graphs 3 Frantǐsek Kardoš Barnette was right: not only fullerene graphs are Hamiltonian 4 Gyula Y. Katona Complexity questions for minimally t-...

Experimental and theoretical studies on fullerene cages are the topic of several investigations in recent years [ 1-l 11. Since the chemistry of fullerenes is increasingly becoming important and theoretical studies of these cages are on the increase it is necessary to have several mathematical procedures for the study of topological properties of these cages. Topological, graph theoretical and ...

A graph G is singular of nullity (> 0), if its adjacency matrix A is singular, with the eigenvalue zero of multiplicity . A singular graph having a 0-eigenvector, x, with no zero entries, is called a core graph.We place particular emphasis on nut graphs, namely the core graphs of nullity one. Through symmetry considerations of the automorphism group of the graph, we study relations among the en...

This paper contains a survey of different methods for generating knots and links based on geometric polyhedra, suitable for applications in chemistry, biology, architecture, sculpture (or jewelry). We describe several ways of obtaining 4-valent polyhedral graphs and their corresponding knots and links from geometrical polyhedra: midedge construction, cross-curve and double-line covering, and ed...

in this research at the first enalapril drug and its fullerene derivative were optimized. nbo calculations and nmr for the complexes were carried out at the b3lyp/6-31g* quantum chemistry level. different parameters such as energy levels, the amount of chemical shift in different atoms, the amount of homo/lumo, chemical potential (µ ), chemical hardness (η), the coefficients of hybrid bonds (π,...