Let C be the unit circle in R. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k > 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 6 k 6 7 what the optima...

introduction: nymphea lotus linn (n. lotus) flowers are used empirically for the treatment of male sexual disorders in cameroon west region. this study was aimed to evaluate the effects of the n. lotus on some parameters of male fertility in adult albino male rats. methods: twenty four male rats were divided in 4 groups (n=6 each) and subjected to the following treatment: distilled water as veh...

We study balanced circle packings and circle-contact representations for planar graphs, where the ratio of the largest circle’s diameter to the smallest circle’s diameter is polynomial in the number of circles. We provide a number of positive and negative results for the existence of such balanced configurations.

We introduce the circle product, a method to construct simple graphs starting from known ones. The circle product can be applied in many different situations and when applied to regular graphs and to their decompositions, a new regular graph is obtained together with a new decomposition. In this paper we show how it can be used to construct infinitely many new solutions to the Oberwolfach probl...

A signed graph is a graph whose edges are signed. In a vertex-signed graph the vertices are signed. The latter is called consistent if the product of signs in every circle is positive. The line graph of a signed graph is naturally vertexsigned. Based on a characterization by Acharya, Acharya, and Sinha in 2009, we give constructions for the signed simple graphs whose naturally vertex-signed lin...

An efficient technology for preparing lotus fibres under microwave irradiation was developed. The lotus fibres were characterized by scanning electron microscopy, Fourier transform infrared spectrometry, X-ray diffraction and thermogravimetry. Lotus fibres prepared are a kind of hollow fibres which are composed of a superfine fibre and an external shell. The effect of the treatment time with hy...

A new short proof is given for Brandt and Harrington's theorem about conformal uniformizations of planar nitely connected domains as domains with boundary components of speciied shapes. This method of proof generalizes to periodic domains. Letting the uniformized domains degenerate in a controlled manner, we deduce the existence of packings of speciied shapes and with speciied combinatorics. Th...

Discovering communities from a graph structure such as the Web has become an interesting research problem recently. In this paper, comparing with the state-of-the-art authority detecting and graph partitioning methods, we propose a concentric-circle model to more accurately define communities. With this model, a community could be described as a set of concentric-circles. The most important obj...

Circular layouts are a popular graph drawing style, where vertices are placed on a circle and edges are drawn as straight chords. Crossing minimization in circular layouts is NP-hard. One way to allow for fewer crossings in practice are two-sided layouts that draw some edges as curves in the exterior of the circle. In fact, oneand two-sided circular layouts are equivalent to one-page and two-pa...

An induced packing of odd cycles in a graph is a packing such that there is no edge in the graph between any two odd cycles in the packing. We prove that the problem is solvable in time O(n ) when the input graph is planar. We also show that deciding if a graph has an induced packing of two odd cycles is NP-complete.