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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 mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. [1] [2] Both directed and undirected versions of rooted graphs have been studied, and there are also variant definitions that allow multiple roots. Examples of rooted graphs with some variants.
A quiver is of finite type if and only if its underlying graph (when the directions of the arrows are ignored) is one of the ADE Dynkin diagrams: , , , , . The indecomposable representations are in a one-to-one correspondence with the positive roots of the root system of the Dynkin diagram.
Every connected graph in which the domination number is half the number of vertices arises in this way, with the exception of the four-vertex cycle graph. These graphs can be used to generate examples in which the bound of Vizing's conjecture , an unproven inequality between the domination number of the graphs in a different graph product, the ...
The current version is a revised version of the original 1960 textbook Physics for Students of Science and Engineering by Halliday and Resnick, which was published in two parts (Part I containing Chapters 1-25 and covering mechanics and thermodynamics; Part II containing Chapters 26-48 and covering electromagnetism, optics, and introducing ...
Photographic recording of Kα and Kβ X-ray emission lines for a range of elements. Moseley's law is an empirical law concerning the characteristic X-rays emitted by atoms.The law was discovered and published by the English physicist Henry Moseley in 1913–1914.
The Feynman Lectures on Physics – another contemporaneously-developed and influential college-level physics series; Course of Theoretical Physics – ten-volume series of books covering advanced theoretical physics, by Lev Landau and Evgeniy Lifshitz; PSSC Physics – a contemporaneously-developed high-school-level physics textbook
A path graph (or linear graph) consists of n vertices arranged in a line, so that vertices i and i + 1 are connected by an edge for i = 1, …, n – 1. A starlike tree consists of a central vertex called root and several path graphs attached to it. More formally, a tree is starlike if it has exactly one vertex of degree greater than 2.