Star (graph theory)

About: Star (graph theory) is a research topic. Over the lifetime, 5328 publications have been published within this topic receiving 54031 citations. The topic is also known as: star & star in graph theory.

Sphere packings I

Abstract: We describe a program to prove the Kepler conjecture on sphere packings. We then carry out the first step of this program. Each packing determines a decomposition of space into Delaunay simplices, which are grouped together into finite configurations called Delaunay stars. A score, which is related to the density of packings, is assigned to each Delaunay star. We conjecture that the score of every Delaunay star is at most the score of the stars in the face-centered cubic and hexagonal close packings. This conjecture implies the Kepler conjecture. To complete the first step of the program, we show that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture.

A Group Theoretic Model for Symmetric Interconnection Networks.

Abstract: The authors develop a formal group-theoretic model, called the Cayley graph model, for designing, analyzing, and improving such networks. They show that this model is universal and demonstrate how interconnection networks can be concisely represented in this model. It is shown that this model enables the authors to design networks based on representations of finite groups. They can then analyze these networks by interpreting the group-theoretic structure graph theoretically, Using these ideas, and motivated by certain well-known combinatorial problems, they develop two classes of networks called star graphs and pancake graphs. These networks are shown to have better performance than previous networks. >

A group-theoretic model for symmetric interconnection networks

Abstract: The authors develop a formal group-theoretic model, called the Cayley graph model, for designing, analyzing, and improving such networks. They show that this model is universal and demonstrate how interconnection networks can be concisely represented in this model. It is shown that this model enables the authors to design networks based on representations of finite groups. They can then analyze these networks by interpreting the group-theoretic structure graph theoretically, Using these ideas, and motivated by certain well-known combinatorial problems, they develop two classes of networks called star graphs and pancake graphs. These networks are shown to have better performance than previous networks. >

Mapping RNA‐seq Reads with STAR

Abstract: Mapping of large sets of high-throughput sequencing reads to a reference genome is one of the foundational steps in RNA-seq data analysis The STAR software package performs this task with high levels of accuracy and speed In addition to detecting annotated and novel splice junctions, STAR is capable of discovering more complex RNA sequence arrangements, such as chimeric and circular RNA STAR can align spliced sequences of any length with moderate error rates, providing scalability for emerging sequencing technologies STAR generates output files that can be used for many downstream analyses such as transcript/gene expression quantification, differential gene expression, novel isoform reconstruction, and signal visualization In this unit, we describe computational protocols that produce various output files, use different RNA-seq datatypes, and utilize different mapping strategies STAR is open source software that can be run on Unix, Linux, or Mac OS X systems