We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n + 1 rungs. Such an assignment yields an index one current graph with current group Z12n+7 that generates an orientable face 2-colorable triangular embedding of the complete graph K12n+7 or, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+7. We use our charact...

Orientable triangular embeddings of the complete tripartite graph Kn,n,n correspond to biembeddings of Latin squares. We show that if n is prime there are at least e ln n−n(1+o(1)) nonisomorphic biembeddings of cyclic Latin squares of order n. If n = kp, where p is a large prime number, then the number of nonisomorphic biembeddings of cyclic Latin squares of order n is at least e ln p−p(1+ln . ...

2014 The energy spectrum of a tight-binding honeycomb lattice in the presence of a uniform magnetic field is analysed. The graph of the spectrum over a wide range of rational reduced flux 03A6/03A60 through elementary hexagonal cells is plotted. The energy spectrum is found to have recursive properties similar to those discussed previously on the square and triangular lattices. New features of ...

Problem statement: In this study researchers propose a new fuzzy graph theoretic construct called fuzzy metagraph and a new method of clustering finding the similar fuzzy nodes in a fuzzy metagraph. Approach: We adopted T-norms (Triangular Norms) functions and join two or more Tnorms to cluster the fuzzy nodes. Fuzzy metagraph is the fuzzyfication of the crisp Metagraphs using fuzzy Generating ...

Norton and Stein associated a number with each idempotent quasigroup or diagonalized Latin square of given finite order n, showing that it is congruent mod 2 to the triangular number T (n). In this paper, we use a graph-theoretic approach to extend their invariant to an arbitrary finite quasigroup. We call it the cycle number, and identify it as the number of connected components in a certain g...

Computing distances among data points is an essential part of many important algorithms in data analytics, graph analysis, and other domains. In each of these domains, developers have spent significant manual e↵ort optimizing algorithms, often through novel applications of the triangle equality, in order to minimize the number of distance computations in the algorithms. In this work, we observe...

In order to avoid interference in cellular telephone networks, sets of radio frequencies are to be assigned to transmitters such that adjacent transmitters are allotted disjoint sets of frequencies. Often these transmitters are laid out like vertices of a triangular lattice in a plane. This problem corresponds to the problem of multicoloring an induced subgraph of a triangular lattice with inte...

〈Summary〉 3D structure of proteins deeply relates to their functionality. It is wellknown that functions of proteins strongly appear in the bumpy parts of the molecular surfaces, and therefore geometric analysis of protein molecular surfaces is important. We propose a technique to extract geometric features of protein molecular surfaces, and a visual interface to effectively visualize the extra...

When the vertices of an n-vertex graph G are numbered by the integers 1 through n, the length of an edge is the difference between the numbers on its endpoints. Two edges overlap if the larger of their lower numbers is less than the smaller of their upper numbers. The bandwidth of G is the minimum, over all numberings, of the maximum length of an edge. The cutwidth of G is the minimum, over all...

We find all maximal linklessly embeddable graphs of order up to 11, and verify that for every graph [Formula: see text] 11 either or its complement is intrinsically linked. give an example a such both are text]-minor free. provide minimal examples not triangular three-connected. prove Nordhaus–Gaddum-type conjecture on the Colin de Verdière invariant at most vertices. description programs used ...