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A (p,q)-torus knot is obtained by looping a string through the hole of a torus p times with q revolutions before joining its ends, where p and q are relatively prime. A ...

A complete oriented graph (Skiena 1990, p. 175), i.e., a graph in which every pair of nodes is connected by a single uniquely directed edge. The first and second 3-node ...

The triangular graph T_n=L(K_n) is the line graph of the complete graph K_n (Brualdi and Ryser 1991, p. 152). The vertices of T_n may be identified with the 2-subsets of ...

The Tucker circles are a generalization of the cosine circle and first Lemoine circle which can be viewed as a family of circles obtained by parallel displacing sides of the ...

A Turán graph, sometimes called a maximally saturated graph (Zykov 1952, Chao and Novacky 1982), with positive integer parameters n and k is a type of extremal graph on n ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...

A vertex-transitive graph, also sometimes called a node symmetric graph (Chiang and Chen 1995), is a graph such that every pair of vertices is equivalent under some element ...

The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation F_n=F_(n-1)+F_(n-2) (1) with F_1=F_2=1. As a result of the ...

Just as many interesting integer sequences can be defined and their properties studied, it is often of interest to additionally determine which of their elements are prime. ...

An arc-transitive graph, sometimes also called a flag-transitive graph, is a graph whose graph automorphism group acts transitively on its graph arcs (Godsil and Royle 2001, ...