On Packing Colouring of Transformation of Path, Cycle and Wheel Graphs

Abstract

Objectives: To compute the packing chromatic number of transformation of path graph, cycle graph and wheel graph. Methods: The packing chromatic number χ pc (H) of a graph H is the least integer m in such a way that there is a mapping C : V (H) → (1, 2, . . . , m} such that the distance between any two nodes of colour k is greater than k + 1. Findings: The packing chromatic number of the transformation of the graph χ pc (H pqr ) where p, q, r be variables which has the values either positive sign (+) or a negative sign (−) then H pqr is known as the transformation of the graph H such that V (H) and E(H) belonging to the vertex set of H pqr and α (H) , β (H) also belonging to V (H) , E (H) of the graph. Obtained the values of the packing chromatic number of transformation of path graph, cycle graph and wheel graph. Applications: Chromatic number applied in Register Allocations, a compiler is a computer program that translates one computer language into another. To improve the execution time of the resulting code, one of the techniques of compiler optimization is register allocation; if the graph can be colored with k colors then the variables can be stored in k registers.

Algorithm Based on Morphological Operators for Shortness Path Planning

“…These approaches are helpful when there is no previous knowledge about the scenario, making them feasible in uncertain environments. The low complexity makes it possible to obtain subgraph partitions and instantiate in several initial states [15][16][17].…”