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.
Abstract: Col is a classic combinatorial game played on graphs
and to solve a general instance is a PSPACE-complete problem.
However, winning strategies can be found for some specific graph
instances. In this paper, the solution of Col on complete k-ary trees
is presented.