Normal forms for binary relations - DCC
... Let ER be the set of equations valid in R. 2.2. Graphs and diagrams A labelled, directed graph is a structure G = (V , E, s, f ) where V is a finite set of vertices, s ∈ V , f ∈ V , and E ⊆ V × 2Vars × V . That is, there is a distinguished start vertex s and a distinguished finish vertex f , not neces ...
... Let ER be the set of equations valid in R. 2.2. Graphs and diagrams A labelled, directed graph is a structure G = (V , E, s, f ) where V is a finite set of vertices, s ∈ V , f ∈ V , and E ⊆ V × 2Vars × V . That is, there is a distinguished start vertex s and a distinguished finish vertex f , not neces ...
Graph Symmetries
... An s-arc in a graph X is a sequence (v0, v1, v2, . . . , vs) of s+1 vertices of X such that {vi−1, vi} is an edge of X for 0 < i ≤ s and vi−1 6= vi+1 for 0 < i < s – or in other words, such that any two consecutive vi are adjacent and any three consecutive vi are distinct. The graph X is called s-ar ...
... An s-arc in a graph X is a sequence (v0, v1, v2, . . . , vs) of s+1 vertices of X such that {vi−1, vi} is an edge of X for 0 < i ≤ s and vi−1 6= vi+1 for 0 < i < s – or in other words, such that any two consecutive vi are adjacent and any three consecutive vi are distinct. The graph X is called s-ar ...
Coloring k-colorable graphs using smaller palletes
... matrix of the squared graph. 3. Find, recursively, the distances in the squared graph. 4. Decide, using one integer matrix multiplication, for every two vertices u,v, whether their distance is twice the distance in the square, or twice minus 1. ...
... matrix of the squared graph. 3. Find, recursively, the distances in the squared graph. 4. Decide, using one integer matrix multiplication, for every two vertices u,v, whether their distance is twice the distance in the square, or twice minus 1. ...
Persistent data structures
... Application -- planar point location Suppose that the Euclidian plane is subdivided into polygons by n line segments that intersect only at their endpoints. Given such polygonal subdivision and an on-line sequence of query points in the plane, the planar point location problem, is to determine for ...
... Application -- planar point location Suppose that the Euclidian plane is subdivided into polygons by n line segments that intersect only at their endpoints. Given such polygonal subdivision and an on-line sequence of query points in the plane, the planar point location problem, is to determine for ...
A11 Quadratic functions - roots, intercepts, turning
... NOTE: The ROOTS of an equation in x means you need to solve the equation to find the values of x. If you have a graph, you can find estimates of x by looking to see where the graph cuts the x-axis. If you are asked to deduce the roots of a quadratic equation algebraically it means you have to use al ...
... NOTE: The ROOTS of an equation in x means you need to solve the equation to find the values of x. If you have a graph, you can find estimates of x by looking to see where the graph cuts the x-axis. If you are asked to deduce the roots of a quadratic equation algebraically it means you have to use al ...
A topological approach to evasiveness | SpringerLink
... whereas the dual of a collapsible complex may fail to be collapsible. (The first o f these assertions is an easy exercise. The second is seen as follows. It is known (see [4], p. 69) that a collapsible A may be collapsed to a noncollapsible 27. On the other hand, it is an easy consequence o f the de ...
... whereas the dual of a collapsible complex may fail to be collapsible. (The first o f these assertions is an easy exercise. The second is seen as follows. It is known (see [4], p. 69) that a collapsible A may be collapsed to a noncollapsible 27. On the other hand, it is an easy consequence o f the de ...
Centrality
In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin.They should not be confused with node influence metrics, which seek to quantify the influence of every node in the network.