PARTITION DIMENSION FOR LINE GRAPH OF HONEYCOMB NETWORKS AND AZTEC DIAMOND NETWORKS

Abstract

In graph theory, a commonly used concept is the partition dimension or partition metric basis is to uniquely identify the node set of a structure by dividing it into smaller subsets, known as partition resolving sets. These subsets can then be used to define the partition dimension or partition metric of the graph. This concept is useful in the analysis and understanding of the structure and properties of graphs. This article describes a partition dimension of the line graph of the honeycomb network, the Aztec diamond network, and the extended Aztec diamond network.