Predicting Mathematical Models using Gracefully Labelled Graphs

Abstract

OBJECTIVES newlineand#61623; To know the importance of Graph Labeling and have complete knowledge of newlineit. newlineand#61623; To know thoroughly the brief history of Graph Theory and understand how newlineGraph Labeling is important. newlineand#61623; To create new Mathematical Models to suggest new solutions in the fields of newlineMathematical Modeling using Graph Theory. newlineand#61623; To understand Graph Theory and Graph Labeling in details so as to use that newlineknowledge to create new Mathematical Graphical Models. newlineand#61623; To use the labeled graphs with their applications in Mathematical Models. newlineand#61623; It has been proved that complete graphs with five or more vertices cannot be newlinegracefully labeled. I want to work in this particular area of researchCONCLUSION newlineand#61623; The business model takes into account three basic Graphical Solution Models newlinethat are Route Inspection Problem, Travelling Salesman Problem and newlineAssignment Problem. The solution of the above drawn logistics model will newlineassign each type of manager the least number of trips travelling least distance newlineso as there is no overlap and repeat meetings. newlineand#61623; The sales area network has been represented as a symmetric and#119896;-ary tree which newlineis gracefully labelled and Graceful Labeling of the and#119896;-ary tree is used to solve newlinethe Travelling Salesman Problem for logistics management of a business. newlineand#61623; Thirdly, we connect Logistical Solution by the means of Graphical newlineRepresentation, Graph Labeling and Path Algorithms. This particular concept newlineis very important to solve many problems of Supply Chain Management. By newlineusing the Travelling Salesman Problem we can create the Least Time Least newlineDistance model for a particular distribution industry. newlineand#61623; Further, we applied the Nearest Neighbour Method of Travelling Salesman newlineProblem to symmetrical tree (to be moulded as a business model) with the aim newlineto find a route with minimum distance and cost or time. newlineand#61623; Our next algorithm takes input as the number of cities and coordinates as the newlinedistances for cities that are represented in the form of an adjacency matrix. If newlinethe starting node is specified it continues with it