We consider Schrödinger operators on threshold graphs and give an explicit construction of a Colin de Verdière matrix for each connected threshold graph G of n vertices. We conclude the Colin de Verdière graph parameter μ(G) satisfies μ(G) ≥ n− i− 1, where i is the number of isolates in the graph building sequence. The proof is algorithmic in nature, constructing a particular Colin de Verdiére ...

The classical DPO graph rewriting construction is re-expressed using the oppbration approach introduced originally for term graph rewriting. Using a skeleton category of graphs, a base of canonical graphs-in-context, with DPO rules as arrows, and with categories of redexes over each object in the base, yields a category of rewrites via the discrete Grothendieck construction. The various possibl...

Sets of mutually orthogonal Latin squares prescribe the order in which to apply different treatments designing an experiment permit effective statistical analysis results, they encode incidence structure finite geometries, encapsulate groups and more general algebraic objects known as quasigroups, produce optimal density error-correcting codes. This paper gives some new results on graph squares...

A framework for planning algorithms that is both optimal and complete will be presented. The algorithm allows for the planning of optimal paths through a multi-level hierarchy of annotated graph spaces. A rich world model that contains multi-resolution attributes, costs, and predicates controls the integrated incremental construction and evaluation of the planning graph in dynamic environments....

Define the middle layer graph as the graph whose vertex set consists of all bitstrings of length 2n + 1 that have exactly n or n + 1 entries equal to 1, with an edge between any two vertices for which the corresponding bitstrings differ in exactly one bit. In this work we present an inductive construction of a large family of 2-factors in the middle layer graph for all n ≥ 1. We also investigat...

Most of Information Retrieval (IR) systems are still based on bag of word paradigm. This is a strong limitation if one needs high precision answers. For example, in restricted domain, like medicine, user builds short and precise query, like “Show me chest CT images with emphysema.”, and expects from the system precise answers. In such a case, the use of natural language processing to model docu...