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The vertex set of an n-vertex graph may be identified with the integers from 1 to n, and using such an identification a canonical form of a graph may also be described as a permutation of its vertices. Canonical forms of a graph are also called canonical labelings, [4] and graph canonization is also sometimes known as graph canonicalization.
graph-tool is a Python module for manipulation and statistical analysis of graphs (AKA networks). The core data structures and algorithms of graph-tool are implemented in C++ , making extensive use of metaprogramming , based heavily on the Boost Graph Library . [ 1 ]
In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edges so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face (or ...
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
For instance, giving each vertex a distinct color would be equitable, but would typically use many more colors than are necessary in an optimal equitable coloring. An equivalent way of defining an equitable coloring is that it is an embedding of the given graph as a subgraph of a Turán graph with the same set of vertices
Graphviz (short for Graph Visualization Software) is a package of open-source tools initiated by AT&T Labs Research for drawing graphs (as in nodes and edges, not as in bar charts) specified in DOT language scripts having the file name extension "gv". It also provides libraries for software applications to use the tools.
The basic operations provided by a graph data structure G usually include: [1] adjacent(G, x, y): tests whether there is an edge from the vertex x to the vertex y; neighbors(G, x): lists all vertices y such that there is an edge from the vertex x to the vertex y; add_vertex(G, x): adds the vertex x, if it is not there;