On Packing Colouring of Transformation of Path, Cycle and Wheel Graphs
R. Srinivasan, M. Vivekanandan
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 (Hpqr) where p,q,r be variables which has the values either positive sign (+)+ or a negative sign (-) then Hpqr is known as the transformation of the graph H such that VH and E(H) belonging to the vertex set of Hpqr 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. Keywords path graph, cycle graph, wheel graph, packing chromatic number