the padmakar-ivan (pi) index is a wiener-szeged-like topological index which reflectscertain structural features of organic molecules. the pi index of a graph g is the sum of alledges uv of g of the number of edges which are not equidistant from the vertices u and v. inthis paper we obtain the second and third extremals of catacondensed hexagonal systems withrespect to the pi index.

the first geometric-arithmetic index was introduced in the chemical theory as the summationof 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertexu. in this paper we give the expressions for computing the first geometric-arithmetic index ofhexagonal systems and phenylenes and present new method for describing hexagonal systemby corresponding a simple graph...

The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...

In this paper, the periodic, quasi periodic and chaotic responses of rotational machines with a hexagonal centrifugal governor are studied. The external disturbance is assumed as a sinusoid effect. By using the forth order Rung-Kutta numerical integration method, bifurcation diagram, largest Lyapunov exponent and Lyapunov dimension are calculated and presented to detect the critical controlling...

OF THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science Computer Science The University of New Mexico Albuquerque, New Mexico

In this paper we introduce hexagonal Wang tiles, local hexagonal picture languages, and recognizable hexagonal picture languages. We use hexagonal Wang tiles to introduce hexagonal Wang systems(HWS), a formalism to recognize hexagonal picture languages. It is noticed that the family of hexagonal picture languages defined by hexagonal Wang systems coincides with the family of hexagonal picture l...

In this paper the Clar covering polynomial of a hexagonal system is introduced. In fact it is a kind of F polynomial [4] of a graph, and can be calculated by recurrence relations. We show that the number of aromatic sextets (in a Clar formula), the number of Clar formulas, the number of Kekule structures and the first Herndon number for any Kekulean hexagonal system can be easily obtained by it...

The interplay between local constraints and global structure of mathematical and physical systems is both subtle and important. The macroscopic physical properties of a system depend heavily on its global symmetries, but these are often difficult to predict given only information about local interactions between the components. A rich history of work on tilings of the Euclidean plane and higher...

Let H be a hexagonal system. The Z-transformation graph Z(H) is the graph where the vertices are the perfect matchings of H and where two perfect matchings are joined by an edge provided their symmetric difference is a hexagon of H (Z. Fu-ji et al., 1988). In this paper we prove that Z(H) has a Hamilton path if H is a catacondensed hexagonal system. A hexagonal system [ll], also called honeycom...

Two-dimensional (2-D) spatially varying convolutional filters for three-dimensional (3-D) depth extrapolation are efficiently designed and implemented by using McClellan transformations. Although efficient, McClellan transformations only approximate circularly symmetric depth extrapolation filters. The accuracy of the extrapolation filters can be increased only at an increase in the computation...