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In the mathematical field of graph theory, a word-representable graph is a graph that can be characterized by a word (or sequence) whose entries alternate in a prescribed way. In particular, if the vertex set of the graph is V , one should be able to choose a word w over the alphabet V such that letters a and b alternate in w if and only if the ...
In molecular spectroscopy, a Jablonski diagram is a diagram that illustrates the electronic states and often the vibrational levels of a molecule, and also the transitions between them. The states are arranged vertically by energy and grouped horizontally by spin multiplicity . [ 1 ]
An undirected graph with three vertices and three edges. In one restricted but very common sense of the term, [1] [2] a graph is an ordered pair = (,) comprising: , a set of vertices (also called nodes or points);
In the mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can be stated as follows: [ 1 ] Let G {\displaystyle G} be a regular graph whose degree is an even number, 2 k {\displaystyle 2k} .
Triangle-free graphs: Triangle K 3: Induced subgraph Definition Planar graphs: K 5 and K 3,3: Homeomorphic subgraph Kuratowski's theorem: K 5 and K 3,3: Graph minor Wagner's theorem: Outerplanar graphs: K 4 and K 2,3: Graph minor Diestel (2000), [1] p. 107: Outer 1-planar graphs: Six forbidden minors Graph minor Auer et al. (2013) [2] Graphs of ...
Jablonski diagram, diagram that illustrates the electronic states of a molecule and the transitions between them Jablonski by Pahls v. United States , a landmark court case that helped to define the ethical duties of mental health professionals with respect to potentially violent individuals.
Let G be a k-regular graph with 2n nodes. If k is sufficiently large, it is known that G has to be 1-factorable: If k = 2n − 1, then G is the complete graph K 2n, and hence 1-factorable (see above). If k = 2n − 2, then G can be constructed by removing a perfect matching from K 2n. Again, G is 1-factorable.
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