We show that there are four infinite prime graphs such that every infinite prime graph with no infinite clique embeds one of these graphs. We derive a similar result for infinite prime posets with no infinite chain or no infinite antichain.

It is well known that a prime link diagram corresponds to a signed plane graph without cut vertices (Kauffman, 1989). In this paper, we present a new relation between prime links and cubic 3-polytopes. Let S be the set of links such that each L ∈ S has a diagram whose corresponding signed plane graph is the graph of a cubic 3-polytope. We show that all nontrivial prime links, except (2, n)-toru...

This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived. Moreover, since most graphs are prime although they can have a product-like structure, also known as approximate graph products, the practical application of the...

We describe in this paper a prototype 1 , PRIME, of a multimedia medical information retrieval system. The documents managed by PRIME are patient records, which are composed of administrative data, textual reports, and Magnetic Resonance Images. PRIME is developed on top of the object oriented DBMS O2, and its interface can be any WWW-navigator (Netscape, InternetExplorer, ...). The retrieval e...

Juggling patterns can be described by a closed walk in a (directed) state graph, where each vertex (or state) is a landing pattern for the balls and directed edges connect states that can occur consecutively. The number of such patterns of length n is well known, but a long-standing problem is to count the number of prime juggling patterns (those juggling patterns corresponding to cycles in the...

In this paper, we study the relationships between graphs and prime spectrum of unitary commutative rings. It is shown that a graph G equipped with G-right topology satisfies some spectral properties. particular give necessarily sufficient condition to obtain graph.

We develop a network in which the natural numbers are the vertices. The decomposition of natural numbers by prime numbers is used to establish the connections. We perform data collapse and show that the degree distribution of these networks scales linearly with the number of vertices. We explore the families of vertices in connection with prime numbers decomposition. We compare the average dist...

A graph monoid is a commutative monoid for which there is a particularly simple presentation, given in terms of a quiver. Such monoids are known to satisfy various nonstable K-theoretical representability properties for either von Neumann regular rings or C*-algebras. We give a characterization of graph monoids within finitely generated antisymmetric refinement monoids. This characterization is...

We introduce and investigate a new class of graphs arrived from exponential congruences. For each pair of positive integers a and b, let G n denote the graph for which V {0, 1, . . . , n − 1} is the set of vertices and there is an edge between a and b if the congruence a ≡ b modn is solvable. Let n p1 1 p k2 2 · · · pr r be the prime power factorization of an integer n, where p1 < p2 < · · · < ...

A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify tetravalent symmetric graphs of order 9p for each prime p.