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An important result in valuation theory which gives information on finding roots of polynomials. Hensel's lemma is formally stated as follows. Let (K,|·|) be a complete ...

The concept of irredundance was introduced by Cockayne et al. (1978). Let N_G[v] denote the graph neighborhood of a vertex v in a graph G (including v itself), and let N_G[S] ...

A rational amicable pair consists of two integers a and b for which the divisor functions are equal and are of the form sigma(a)=sigma(b)=(P(a,b))/(Q(a,b))=R(a,b), (1) where ...

The rational distance problem asks to find a geometric configuration satisfying given properties such that all distances along specific edges are rational numbers. (This is ...

An n-polyhedral graph (sometimes called a c-net) is a 3-connected simple planar graph on n nodes. Every convex polyhedron can be represented in the plane or on the surface of ...

B-trees were introduced by Bayer (1972) and McCreight. They are a special m-ary balanced tree used in databases because their structure allows records to be inserted, ...

A semicubical parabola is a curve of the form y=+/-ax^(3/2) (1) (i.e., it is half a cubic, and hence has power 3/2). It has parametric equations x = t^2 (2) y = at^3, (3) and ...

A Lucas cube graph of order n is a graph that can be defined based on the n-Fibonacci cube graph by forbidding vertex strings that have a 1 both in the first and last ...

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 ...

The cube-connected cycle graph of order n is the graph obtained by replacing each vertex in a n-dimensional hypercube by a cycle of length n. They were introduced by ...