Development of models for transformation of connected graphs into single-row networks

Abstract

In this paper, we present a collection of models for connected graphs mapping into single-row networks. The collection involves three specific models for perfect binary trees, trees and partially dense graphs, and three general models for connected graphs. These models are compared in terms of their structures, energy values, congestion and number of doglegs in the single-row transformation. The numerical experiments are run by each respective developed program. The transformation is necessary in applications such as in the assignment of telephone channels to caller-receiver pairs roaming in cells in a cellular network on real-time basis.