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
Highlights
Graph theory in mathematics means the study of graphs
We enumerate the packing chromatic number of transformation of path graph, the packing chromatic number of transformation of cycle graph and derived the packing chromatic number of transformation of wheel graph using the definition of transformation of graph
The packing chromatic number for the Cartesian product of the transformation of graphs is under investigation
Summary
Graph theory in mathematics means the study of graphs. Graphs are one of the major areas of Discrete Mathematics. The intention of the packing chromatic number of a graph was established in[1] by Goddard et al There will be more difficult to identify the points in a mesh where two non-identical points are managing the unchanged frequency unless both the points are positioned not to very close. With this representation all points are positioned at nodes in the i packing, Xi, are authorized to convey the uniform repetition only after distance i, this ideology has been developed a lot and used in many fields such as biological diversity, resource placements and so on. Derya et al[6] discussed the packing chromatic number of transformation of graphs
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