Adding Edges between One Node and Every Other Node with the Same Depth in a Complete K-ary Tree

Abstract

This paper proposes a model of adding relations between members of the same level in a pyramid organization structure which is a complete K-ary tree such that the communication of information between every member in the organization becomes the most efficient. When edges between one node and every other node with the same depth N in a complete K-ary tree of height H are added, an optimal depth N∗ = H is obtained by minimizing the total path length which is the sum of lengths of shortest paths between every pair of all nodes. Keywords—complete K-ary tree, organization structure, shortest path