CONTRIBUTIONS TO SOME TOPICS IN THE THEORY OF SIGNED GRAPHS

Abstract

There are several reasons for the acceleration of interest in graph the ory. It is worth to mention that there are applications of graph theory in various areas of physics, chemistry, communication science, comput er technology, electrical and civil engineering, architecture, operational research, genetics, psychology, sociology and economics. Graph theory is also intimately related to many branches of mathematics, including group theory, matrix theory, numerical analysis, probability, topology, combinatorics etc. The fact is that graph theory serve as a mathemat ical model for any system involving a binary relation. Due to diagram matic representation, graphs have an intuitive and aesthetic appeal. Although there are many results in this field of an elementary nature, there is also an abundance of problems with enough combinatorial sub tlety to challenge the most sophisticated mathematician. Signed graph theory forms one of the most vibrant areas of research due to its link with behavioral and social sciences as evident from the published literature; research-level journals like the Journal of Math ematical Sociology, Journal of Mathematical Psychology, Social Net works, Journal of Mathematical Chemistry etc., are only a few notable ones that can be mentioned in this context. In our excursion of re search, we were mainly driven to carry out work in the area of signed graphs derived under some operations, which mainly deals with the 1 structural reconfigurations of the structure of dynamical systems un der prescribed rules and rules are designed to deal with a variety of interconnections among the elements of the system. We were able to obtain some theoretical results which led us to the area of research in the theory of signed graphs with a hope to build necessary conceptual resources for applications.