Functional Product of Graphs and Multiagent Systems (Global Journal of Science Frontier Research, 2017)
In this work, the concepts of functional product of graphs and equitable total coloring were used to propose a model of connection among the multiagent systems. We show how to generate a family of regular graphs that admits a range vertex coloringof order ∆ with ∆ + 1 colors, denominated harmonic graphs. We prove that the harmonic graphs do not have cut vertices. We also show that the concept of equitable total coloring can be used to elaborate parallel algorithms that are independent of the network topology. Finally, we show a model of connection among multiagent systems (MAS) based on the use of harmonic graphs as a support for the construction of P2P overlay network topologies used for the communication among these systems.
Keywords: functional product of graphs; harmonics graphs; multiagent system