ALGEBRA What is Algebra? Algebra helps solve the mathematical equations and allows to derive unknown quantities, like the bank interest, proportions, percentages. We can use the variables in the algebra to represent the unknown quantities that are coupled in such a way as to rewrite the equations. The algebraic formulas are used in our daily lives to find the distance and volume of containers and figure out the sales prices as and when needed. Algebra is constructive in stating a mathematical equation and relationship by using letters or other symbols representing the entities. The unknown quantities in the equation can be solved through algebra. Some of the main topics coming under algebra include Basics of algebra, exponents, simplification of algebraic expressions, polynomials, quadratic equations, etc Branches of Algebra As it is known that, algebra is the concept based on unknown values called variables. The important concept of algebra is equations. It follows various...
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APPLICATIONS OF GRAPH THEORY
Applications [ edit ] The network graph formed by Wikipedia editors (edges) contributing to different Wikipedia language versions (vertices) during one month in summer 2013. [6] Graphs can be used to model many types of relations and processes in physical, biological, [7] [8] social and information systems. [9] Many practical problems can be represented by graphs. Emphasizing their application to real-world systems, the term network is sometimes defined to mean a graph in which attributes (e.g. names) are associated with the vertices and edges, and the subject that expresses and understands real-world systems as a network is called network science . Computer science [ edit ] Within computer science , causal and non-causal linked structures are graphs that are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. For instance, the link structure of a website c...
PRIM’S ALGORITHM
PRIM’S ALGORITHM Prim’s algorithm is a greedy algorithm that is used to find a minimum spanning tree (MST) of a given connected weighted graph. This algorithm is preferred when the graph is dense. The dense graph is a graph in which there is a large number of edges in the graph. This algorithm can be applied to only undirected connected graph and there should not be any negative weighted edge. In this case, the algorithm is quite efficient. Since there are no non-negative weight cycles, there will be a shortest path whenever there is a path. The steps to find minimum spanning tree using Prim’s algorithm are as follows: 1. If graph has loops and parallel edges than remove loops and parallel edges of that graph. 2. Randomly choose any node, labelling it with a distance of 0 and all other nodes as ∞. The chosen node is treated as current node and considered as visited. All other nodes are considered as unvisited....