Introduction To Graph Theory
INTRODUCTION
Graph theory was born in 1736 when Euler, “The father of graph theory’’ solved Konigsberg Bridge problem.
In 1847 Kirchhoff developed the theory of trees in order to solve the system of simultaneous linear equations which give the current in each branch and around each circuit of an electrical network. THE KONIGSBERG BRIDGE PROBLEM:
Konigsberg (55.2 o North latitude and 22 o East longitude) was a city in Russia situated on the Pregel River, which served as the residence of the dukes of Prussia in the 16th century. Today, the city named Kaliningrad, is in Lithuania which recently separated from U.S.S.R. It serves as a major industrial and commercial centre of western Russia. The river Pregel flowed through the town, dividing
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Networks have many uses in the practical side of graph theory, network analysis for example, to model and analyze traffic networks.
Graph theory is also used to study molecules in chemistry and physics. In condensed matter physics, the three dimensional structure of complicated simulated atomic structures can be studied quantitatively by gathering statistics on graph-theoretic properties related to the topology of the atoms.
In transport geography most networks have an obvious spatialfoundation, namely road, transit and rail networks, which tend to defined more by their links than by their nodes. This it is not necessarily the case for alltransportation networks.
Mobile telephone networks or the Internet, possibly to most complex graphs to be considered, are relevant cases of networks having a structure that can be difficult to symbolize. Applications of graph theory are primarily, but not exclusively, concerned with labeled graphs and various specializations of these.
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EQUITABLE DOMINATION More than 50 types of domination parameters have been studied by different authors. Acharya B.D., Sampathkumar E., and Waliker H.B. are some Indian Mathematicians who have made substantial contribution to the study of domination in graphs.In 1979 they published a technical report “Recent developments in the theory of domination in graphs, Technical Report 14 MRI” which triggered a considerable amount of research in this area.
Swaminathan et al10. introduced the concept of equitable domination in graphs, by considering the following real world problems; In a network, nodes with nearly equal capacity may interact with each other in a better way. In the society, persons with nearly equal status, tend to be friendly. In an industry, employees with nearly equal powers form association and move closely. Equitability among citizens in terms of wealth, health, status etc is the goal of a democratic nation. In order to study this practical concept, a graph model is to be created. This dissertation deals with the concepts of Equitable Covering, Equitable Packing, Equitable Full Sets and Adjacency Inherent Equitable Graph have been explained with elementary examples and
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