Indian Journal of Science and Technology

Abstract

Objectives: To compute the packing chromatic number of transformation of path graph, cycle graph and wheel graph. Methods: The packing chromatic number of  Xpc (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 Xpc (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 VH
 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.