It was shown by Gerhard Ringel that one of the three non-isomorphic Steiner triple systems of order 15 having an automorphism of order 5 may be biembedded as the faces of a face 2-colourable triangular embedding of K15 in a suitable orientable surface. Ringel’s bi-embedding was obtained from an appropriate current graph. In a recent paper, the present authors showed that a second STS(15) of thi...

A pseudo-triangulation on a closed surface without loops is a graph embedded on the surface so that each face is triangular and may have multiple edges, but no lo $0$ps. We shall establish a theory of diagonal flips in those pseudotriangulations. Our theory will work in parallel to that for simple triangulations basically, but it will present more concrete theorems than the latter.

A simple graph model is developed for binary digibl pictures on &triangular grid leading to consistent and intuitive definitions of connectivity and region boundaries as well as fast memory-efficient algorithms for computing boundaries and the "insidedness" tree. Boundary encodings are extremely compact and can be smoothed using a discrete implementation of minimumperimeter polygon methods. Att...

We enumerate all possible trades which involve up to six faces of the face set of a triangular embedding of a simple connected graph. These are classified by the underlying combinatorial trade on the associated block design, and by the geometrical arrangement of the faces necessary to avoid creation of a pseudosurface in the trading operation. The relationship of each of these trades to surface...

The Fuzzy logic concept is implemented in several image processing operations such as edge detection, segmentation, object recognition, etc. In this paper, a novel Image encryption algorithm based on multiple fuzzy graph (FG) mapping technique is proposed. The Fuzzy graphs are obtained from a matrix of size n and then they are used to encrypt an image. Here fuzzy graphs with triangular and sigm...

The title complex, [Ag3Br2(C25H22P2)3]Br·C7H8N2S, comprises a trinuclear [Ag3Br2(C25H22P2)3](+) unit, a Br(-) anion and one N,N'-di-methyl-thio-urea mol-ecule (ptu). Three Ag(I) ions are linked via two μ3-bridging Br atoms, leading to a distorted triangular bipyramid with an Ag⋯Ag separation range of 3.1046 (6)-3.3556 (6) Å. The triangular Ag3 arrangement is stabilized by six P atoms from three...

Sparse triangular solution ooers a challenging irregular problem for parallel systems. The repeated solution of the system Lx = b, where L is a lower triangular factor of a sparse matrix, arises in numerous applications. A previous study 1] has shown that, if L is an incomplete factor, Lx = b can be eeciently solved on a parallel system through substitution. This was accomplished by representin...

Path selection is one of the critical aspects in emergency evacuation. In a fire scene, how to choose an optimal evacuation path for firefighters is a challenging aspect. In this paper, firstly, a dynamic triangular network model formed by robots is presented. On the basis of this model, directed graph is established in order to calculate direct paths. Then multiparameter information fusion whi...

Multiclass data visualizations allow viewers to compare one dataset to another. The visual marks that represent these datasets, or classes, are visually distinguished from one another by easily perceived visual feature differences, such as color or shape. A designer of a graph or map might encode one class of marks as either red, or circular, and another class as either blue, or triangular. One...

This chapter provides a general description of a variational graph-theoretic formulation for simulation of flexible multibody systems (FMS) which includes a brief review of linear graph principles required to formulate this algorithm. The system is represented by a linear graph, in which nodes represent reference frames on flexible bodies, and edges represent components that connect these frame...