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156.768  Articles
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Hierarchical data structures are important for many computing and information science disciplines including data mining, terrain modeling, and image analysis. There are many specialized hierarchical data management systems, but they are not always availab... see more

Given a bijection ? : V(G) ? {1,2, …,|V(G)|}, we associate 2 integers S = ?(u)+?(v) and D = |?(u)-?(v)| with every edge uv in E(G). The labeling ? induces an edge labeling ?' : E(G) ? {0,1} such that for any edge uv in E(G), ? '(uv)=1 if gcd(S,D)=1, and ?... see more

Let G(V,E) be a simple graph and f be a bijection f : V ? E ? {1, 2, …, |V|+|E|} where f(V)={1, 2, …, |V|}. For a vertex x ? V, define its weight w(x) as the sum of labels of all edges incident with x and the vertex label its... see more

This study examined a game-based teaching activity on "Factors and Multiples" designed for the 6th grade students. The game aims to create a differentiated and enriched learning environment targeted the curriculum standard “The students determine prime nu... see more

All mathematics of placement in this paper is mathematically absolute and precise by clear mathematics. This paper(section1) is the very basic “synopsis” of an upcoming book by the author “The God of Papa Einstein and Sir Isaac Newton “. It delineates the... see more

We study some properties of structure of the multiplicative group Z*mZ^*_m, in case when m is Mersenne prime, Fermat or Carmichael number. Using the results of these studies, we obtain properties of Mersenne primes, Fermat and Carmichael numbers.

Let R be a finite commutative ring with identity and P be a prime ideal of R. The vertex set is R - {0} and two distinct vertices are adjacent if their product in P. This graph is called the prime ideal gr... see more

 An L(2,1)-labeling of a graph G is a function f  from the vertex set V(G) to the set of all nonnegative integers such that | f (x)- f (y)| = 2 if d(x, y) = 1 and | f (x) - f (y)| = 1 if d(x, y) = 2. The L(2,1)-labeling number ?(G) of G is the s... see more

Context. Ensuring high-speed calculation by computer systems of the classical task of factorization of integer value on simple factorsrequires the development of effective algorithmic methods using the latest information technologies. Fast computation of ... see more

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