Date of Award
Master of Science (MS)
Metric dimension, resolving sets and edge metric dimension are very important invariants for the resolvability of graphs that have been studied and investigated intensively in the literature over the last decades. Their immense utilization in network topology, master mind games, robot navigation and representation of chemical compounds make their study very attractive. This thesis is concerned with the graph-theoretic properties of certain families of connected graphs related to their edge metric dimension. The main objective of this thesis is to study the comparison of metric dimension ver-sus edge metric dimension of certain families of graphs. The study investigates the relationship between the metric and edges metric dimension of flower snarks graphs, hexagonal Möbius graphs, and octagonal Möbius graphs. The study shows different inequalities results based on the structure of graphs. The comparison between metric and edge metric dimensions of the graph will give a better understanding of the properties of these investigated families of graphs.
Bisharat, Sanabel Mahmoud Y., "PROPERTIES OF CERTAIN CONNECTED GRAPHS RELATED TO THEIR EDGE METRIC DIMENSION" (2022). Theses. 931.