AUM Block Coloring for some Perfect Trees

Abstract

Graph coloring is one of the important fields of study in graph theory, with the coloring techniques applied to heterogeneous fields, including human resource management, time management, telecommunications, etc. The new innovative coloring approach AUM block coloring introduced by the authors is being continued for perfect trees in this paper.
For perfect binary trees of level 1,2,3 AUM block chromatic number is obtained and the generalization of results upto n is also given. For perfect ternary trees of level 1,2,3 AUM block chromatic number is established. The results are generalized upto level n perfect ternary trees. Extending the results to n-ary trees in general, AUM block chromatic number for perfect n-ary trees of level 1,2,3 is computed. The generalization upto n is also presented with suitable examples, wherever necessary.