It is known that the set of all convex sets of a finite connected graph together with empty set partially ordered by set inclusion relation forms a lattice. Also the set of all path sets of a finite connected graph together with the empty set partially ordered by set inclusion relation ...
The Hadwiger–Nelson problem concerns the chromatic number of these graphs.An intersection graph is a graph in which each vertex is associated with a set and in which vertices are connected by edges whenever the corresponding sets have a nonempty intersection. When the sets are geometric objects,...
Suppose we have obtained a set of M interest points X={xi}i=1M from the moving image and N interest points Y={yj}j=1N from the fixed image. Feature matching aims to establish correct feature correspondences from two extracted feature sets; this step can be conducted in an indirect or di...
In this section, the terminology and data structures of graphs will first be introduced. Then, some of the most frequently used graph algorithms will be presented. 4.3.1 Terminology A graph G is defined by two sets: a vertex set V and an edge set E. Customarily, a graph is denoted ...
Machine learning plays an increasingly important role in many areas of chemistry and materials science, being used to predict materials properties, accelerate simulations, design new structures, and predict synthesis routes of new materials. Graph neural networks (GNNs) are one of the fastest growing ...
In the inspector there are a number of variables. The first one is named "Convex", it sets if the convex hull of the points should be calculated or if the polygon should be used as-is. Using the convex hull is faster when applying the changes to the graph, but with a non-convex po...
Zhang, Convex sets in graphs. Congr. Numer. 136, 19–32 (1999) MathSciNet MATH Google Scholar G. Chartrand, P. Zhang, On the chromatic dimension of a graph. Congr. Numer. 145, 97–108 (2000) MathSciNet MATH Google Scholar G. Chartrand, P. Zhang, The theory and applications of...
More properties of these sets of states (e.g., concerning the convex structure and extremal points) can be found in refs. 25,27. Three-qudit GHZ states and the inflation technique The inflation technique37 turns out to be an useful tool to study network entanglement25,27. Unless otherwise ...
Problem (16.3) is fundamental in the graph signal processing and statistical machine learning fields and has served as a cornerstone for many extensions, primarily those involving the inference of structure onto the Laplacian matrix L [17,28,42]. Even though problem (16.3) is convex, provided we...
All such problems are solved for the geodesic and monophonic convexities. On the other hand, for the Cayley distance of permutations, we study convexity of sets and interval determination of sets, in the context of the geodesic convexity.