Cooperation means a donor pays a cost, c, for a recipient to get a benefit b. In evolutionary biology, cost and benefit are measured in terms of fitness. While mutation and selection represent the main ‘forces’ of evolutionary dynamics, cooperation is a fundamental principle that is required for every level of biological organization. Individual cells rely on cooperation among their components....

Graph transformations are a powerful notation formally describing different aspects of modeled systems. Multiagent systems introduce distribution, parallelism and autonomous decision properties. In the paper a basic properties of the GRADIS agent’s framework, joining of both approaches, are discussed. This framework supports splitting the graph, describing a problem, onto a few partial graphs, ...

The study of multiagent distributed systems through the optics of the theory of formal grammars and languages is presented. Models based on NLC and BNLC graph grammars are mainly considered. The basic intuition of a grammar model of distributed systems follows the blackboard model for problem solving and is the following: component grammars forming the distributed system execute rewritings on a...

The main purpose of this article – is the systematization of stages and trends of the sociology of education development in Ukraine. The article solves problems of separating the stages of development of this branch of sociology in Ukraine, the personification of their frameworks and the analysis of the research methodology used. The results of the research were obtained from use of the histori...

Cooperation coexisting with defection is a common phenomenon in nature and human society. Previous studies for promoting cooperation based on kin selection, direct and indirect reciprocity, graph selection and group selection have provided conditions that cooperators outcompete defectors. However, a simple mechanism of the long-term stable coexistence of cooperation and defection is still lacki...

Abstract This paper is concerned with a model in econophysics, the subfield of statistical physics that applies concepts from traditional physics to economics. In our model, economical agents are represented by the vertices of a connected graph and are characterized by the number of coins they possess. Agents independently spend one coin at rate one for their basic need, earn one coin at a rate...

Paul Erdos defined the concept of coprime graph and studied about cycles in coprime graphs. In this paper this concept is generalized and a new graph called Generalized coprime graph is introduced. Having observed certain basic properties of the new graph it is proved that the chromatic number and the clique number of some generalized coprime graphs are equal.

Let graph energy is a graph--spectrum--based quantity‎, ‎introduced in the 1970s‎. ‎After a latent period of 20--30 years‎, ‎it became a popular topic of research both‎ ‎in mathematical chemistry and in ``pure'' spectral graph theory‎, ‎resulting in‎ ‎over 600 published papers‎. ‎Eventually‎, ‎scores of different graph energies have‎ ‎been conceived‎. ‎In this article we...

Let $G$ be a simple graph with vertex set ${v_1,v_2,ldots,v_n}$. The common neighborhood graph (congraph) of $G$, denoted by $con(G)$, is the graph with vertex set ${v_1,v_2,ldots,v_n}$, in which two vertices are adjacent if and only they have at least one common neighbor in the graph $G$. The basic properties of $con(G)$ and of its energy are established.