A Note on Degree Partition Number of a Graph
N. Malathi, M. Bhuvaneshwari, Selvam Avadayappan · Journal of Emerging Technologies and Innovative Research · 2021
In pandemic period, there is a need to execute any system with partitioned labours in which every class in a partition shares more or less same potential. Let π_k={V_1,V_2,…,V_k} be a partition of vertex set V of a graph G. Then π_k is called similar degree partition if the sum of degrees of vertices in each class V_i,1≤i≤k, differs from that of other by at most 1. The degree partition number of G, ψ_D (G)=max{k/π_k is a similar degree partition of G} or 1 if no such π_k exists. In this paper, we initiate the study on this parameter and prove some interesting facts.