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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.
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
A graph has a k-coloring if and only if it has an acyclic orientation for which the longest path has length at most k; this is the Gallai–Hasse–Roy–Vitaver theorem (Nešetřil & Ossona de Mendez 2012). For planar graphs, vertex colorings are essentially dual to nowhere-zero flows. About infinite graphs, much less is known.
A graph is contraction-apex if there is some edge in the graph that can be contracted to make the graph planar. In general, if X is a class of graphs, an "apex-X" graph is a graph that can be brought into the class X by deleting some one vertex. For example, an apex-cograph is a graph G that has a vertex v such that G―v is a cograph.
In the mathematical field of graph theory, the Folkman graph is a 4-regular graph with 20 vertices and 40 edges. It is a regular bipartite graph with symmetries taking every edge to every other edge, but the two sides of its bipartition are not symmetric with each other, making it the smallest possible semi-symmetric graph . [ 1 ]
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. [1]
To convert the standard form to factored form, one needs only the quadratic formula to determine the two roots r 1 and r 2. To convert the standard form to vertex form, one needs a process called completing the square. To convert the factored form (or vertex form) to standard form, one needs to multiply, expand and/or distribute the factors.
Coxeter's notation for the same graph would be {n} + {n/k}, a combination of the Schläfli symbols for the regular n-gon and star polygon from which the graph is formed. The Petersen graph itself is G(5, 2) or {5} + {5/2}. Any generalized Petersen graph can also be constructed from a voltage graph with two vertices, two self-loops, and one ...