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AP World History: Modern was designed to help students develop a greater understanding of the evolution of global processes and contacts as well as interactions between different human societies. The course advances understanding through a combination of selective factual knowledge and appropriate analytical skills.
The induced width of an ordered graph is the width of its induced graph. [2] Given an ordered graph, its induced graph is another ordered graph obtained by joining some pairs of nodes that are both parents of another node. In particular, nodes are considered in turn according to the ordering, from last to first. For each node, if two of its ...
A metric space defined over a set of points in terms of distances in a graph defined over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is connected. The eccentricity ϵ(v) of a vertex v is the greatest distance between v and any other vertex; in ...
clique-width The clique-width of a graph G is the minimum number of distinct labels needed to construct G by operations that create a labeled vertex, form the disjoint union of two labeled graphs, add an edge connecting all pairs of vertices with given labels, or relabel all vertices with a given label. The graphs of clique-width at most 2 are ...
Construction of a distance-hereditary graph of clique-width 3 by disjoint unions, relabelings, and label-joins. Vertex labels are shown as colors. In graph theory, the clique-width of a graph G is a parameter that describes the structural complexity of the graph; it is closely related to treewidth, but unlike treewidth it can be small for dense graphs.
The graphs G i may be taken as the induced subgraphs of the sets X i in the first definition of path decompositions, with two vertices in successive induced subgraphs being glued together when they are induced by the same vertex in G, and in the other direction one may recover the sets X i as the vertex sets of the graphs G i. The width of the ...
Branch decomposition of a grid graph, showing an e-separation.The separation, the decomposition, and the graph all have width three. In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree T with the edges of G as its leaves.
The carving width is only one of several graph width parameters that measure how tree-like a given graph is. Others include the treewidth and branchwidth.The branchwidth of a graph is defined similarly to carving width, using hierarchical clusterings, but of the edges of a graph rather than of its vertices; these are called branch-decompositions.