There are two approaches for simulating memory as well as learning in artificial intelligence; the functionalistic approach and the cognitive approach. The necessary condition to put the second approach into account is to provide a model of brain activity that contains a quite good congruence with observational facts such as mistakes and forgotten experiences. Given that human memory has a solid core that includes the components of our identity, our family and our hometown, the major and determinative events of our lives, and the countless repeated and accepted facts of our culture, the more we go to the peripheral spots the data becomes flimsier and more easily exposed to oblivion. It was essential to propose a model in which the topographical differences are quite distinguishable. In our proposed model, we have translated this topographical situation into quantities, which are attributed to the nodes. The result is an edge-weighted graph with mass-based values on the nodes which demonstrates the importance of each atomic proposition, as a truth, for an intelligent being. Furthermore, it dynamically develops and modifies, and in successive phases, it changes the mass of the nodes and weight of the edges depending on gathered inputs from the environment.

We prove that the graph obtained from the non-nilpotent graph of a finite group by deleting the isolated vertices is connected with diameter at most 3. This bound is the best possible.

The diameter of a connected graph G, denoted by diam (G), is the maximum distance between any pair of vertices of G. Let L (G) be the line graph of G. We establish necessary and sufficient conditions under which for a given integer k³2, diam (L(G))£k.

The energy, E(G), of a simple graph G is defined to be the sum of the absolute values of the eigen values of G. In this paper, we introduce some in-equalities of energy of graphs.

In this paper, we construct a new class of integral bipartite graphs (not necessarily trees) with large even diameters. In fact, for every nite set A of positive integers of size k we construct an integral bipartite graph G of diameter 2 k such that the set of positive eigenvalues of G is exactly A. This class of integral bipartite graphs has never found before.

Let R be a commutative ring with identity and let M be an R-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between some algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete, tree or complete bipartite are studied and several characterizations are given.

In this paper we introduce and study a graph on the set of ideals of a commutative ring RR. The vertices of this graph are non-trivial ideals of RR and two distinct ideals II and JJ are adjacent if and only IJ=I∩ JIJ=I∩ J. We obtain some properties of this graph and study its relation to the structure of RR.