Consider a graph G in which each vertex is either a supply vertex or a demand vertex and is assigned a supply or a demand. Such a graph G is called a power supply network. All the supplies and demands are nonnegative constant numbers in an ordinary network, called a steady network [1].This thesis introduces a parametric power supply network, in which all the supplies and demands are functions o...

We present several characterizations of circle graphs, which follow from Bouchet’s circle graph obstructions theorem.

Accurately detection of retinal landmarks, like optic disc, is an important step in the computer aided diagnosis frameworks. This paper presents an efficient method for automatic detection of the optic disc’s center and estimating its boundary. The center and initial diameter of optic disc are estimated by employing an ANN classifier. The ANN classifier employs visual features of vessels and th...

We analyze Hotelling’s duopoly model on the plane. There are two players (firms) located in different points inside a circle and the customers are distributed with some density in it. The solution of two game-theoretic problems is derived. The first problem is to find the equilibrium prices for the homogeneous goods, and the second problem is to find the equilibrium allocation of the players in...

 The problem of suppressing zero-input limit cycles in coupled-form state-space digital filters when the quantization is performed just after the multiplication is here addressed. No proof has been presented guaranteeing that zero-input limit cycles are not sustained in the filter output when the poles are placed anywhere inside the unit circle. Some authors have addressed this topic, but the ...

this paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. first, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. this new algorithm ca...

An interval graph is the intersection graph of a finite set of intervals on a line and a circular-arc graph is the intersection graph of a finite set of arcs on a circle. While a forbidden induced subgraph characterization of interval graphs was found fifty years ago, finding an analogous characterization for circular-arc graphs is a long-standing open problem. In this work, we study the inters...

We state a sufficient condition for the square of a locally finite graph to contain a Hamilton circle, extending a result of Harary and Schwenk about finite graphs. We also give an alternative proof of an extension to locally finite graphs of the result of Chartrand and Harary that a finite graph not containing K4 or K2,3 as a minor is Hamiltonian if and only if it is 2-connected. We show furth...

It is known that every triangle-free (equivalently, of girth at least 4) circle graph is 5-colourable (Kostochka, 1988) and that there exist examples of these graphs which are not 4-colourable (Ageev, 1996). In this note we show that every circle graph of girth at least 5 is 2-degenerate and, consequently, not only 3-colourable but even 3-choosable.