Using two backtrack algorithms based on different techniques, designed and implemented independently, we were able to determine up to isomorphism all strongly regular graphs with parameters v = 45, k = 12, λ = μ = 3. It turns out that there are 78 such graphs, having automorphism groups with sizes ranging from 1 to 51840.

This paper presents a fully automatic segmentation method for the virtual bronchoscopy, which requires the segmentation of a trachea and left/right bronchi. A trachea region is automatically detected, based on medical knowledge and DICOM header information, and its center point is selected as a seed point for the slice-based 3D Seeded Region Growing(SRG). The slice-based 3D SRG grows a region b...

A biplane is a 2-(k(k − 1)/2 + 1, k, 2) symmetric design. Only sixteen nontrivial biplanes are known: there are exactly nine biplanes with k < 11, at least five biplanes with k = 11, and at least two biplanes with k = 13. It is here shown by exhaustive computer search that the list of five known biplanes with k = 11 is complete. This result further implies that there exists no 3-(57, 12, 2) des...

We use nonstandard topology and the g-topology to characterize normal, almost-normal, regular, almost-regular, semiregular spaces. The cluster [resp. 0-cluster] set relation is used to characterize regular, almostregular [resp. strongly-regular] spaces. The Whyburn [resp. Dickman] filter bases are characterized and it is shown that the cluster [resp. f-cluster] set relation restricted to the do...

We present an algorithm for a construction of strongly regular families of trian-gulations for planar domains with a piecewise smooth boundary. Some additional properties of resulting triangulations are considered.