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For graphs that are allowed to contain loops connecting a vertex to itself, a loop should be counted as contributing two units to the degree of its endpoint for the purposes of the handshaking lemma. [2] Then, the handshaking lemma states that, in every finite graph, there must be an even number of vertices for which is an odd number. [1]
4.1 Graph theory. 4.2 Order theory. ... Download as PDF; Printable version; In other projects Wikidata item; ... Handshaking lemma; Kelly's lemma;
The degree sum formula states that, given a graph = (,), = | |. The formula implies that in any undirected graph, the number of vertices with odd degree is even. This statement (as well as the degree sum formula) is known as the handshaking lemma. The latter name comes from a popular mathematical problem, which is to prove that in any group ...
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From the handshaking lemma, a k-regular graph with odd k has an even number of vertices. A theorem by Nash-Williams says that every k ‑regular graph on 2k + 1 vertices has a Hamiltonian cycle. Let A be the adjacency matrix of a graph. Then the graph is regular if and only if = (, …,) is an eigenvector of A. [2]
Download as PDF; Printable version; In other projects ... Help. Pages in category "Lemmas in graph theory" The following 5 pages are in this category, out of 5 total ...
The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics.It provides one of two known approaches to solving the graph realization problem, i.e. it gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph.
In mathematics, the Lindström–Gessel–Viennot lemma provides a way to count the tuples of non-intersecting lattice paths, or, more generally, paths on a directed graph. It was proved by Gessel–Viennot in 1985, based on previous work of Lindström published in 1973. The lemma is named after Bernt Lindström, Ira Gessel and Gérard Viennot.
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