A Visual Tool for Determining the Maximum Independant Set of a Graph Using the Polynomial Formulation Method
Maximum independent set is a prototype problem in a graph theory that has many applications in engineering and science. In this paper, we study the problem of determining the largest number of maximum independent sets of a graph G (V, E) of order n using polynomial formulations. This method uses the first and second order neighbourhoods of nodes to determine whether a node is in the maximum independent set. This involves the maximization of an n-variable polynomial, where n is the number of nodes in G. Finally, we present a visual tool developed using the Visual C++ programming language for solving the maximum independent set problem.
This paper treats optimal design of an elastic truss subject to alternative loads and stress constraints. Necessary and sufficient conditions for local optimality of a fully stressed design are derived by the method of Lagrange multipliers. These criteria provide practical means of determining whether a given fully stressed design is or is not optimal.