Some Wheel Related Graph and It's Local Edge Metric Dimension

Abstract

One of the mathematics branches that often used in daily life as a tool to make the models of problem easier to understand and solved is graph theory. One of the topic in graph theory is metric dimension. The extension of the metric dimension theory is a local edge metric dimension. Let the metric generator of graph � be a vertex � ∈ �, � is a non empty set, therefore for any two edges in graph G namely �1 and �2, we have d_�(�, �# ≠ �$(�, �%)). The edge metric dimension of graph � is the minimum edge metric generator. In line with the concept of edge metric dimension, the local edge metric dimension is the development of edge metric dimension with special requirement. For every adjacent edges �� and �� in graph�, if it full fill �(��|�) ≠ �(��|�), the minimum cardinality of � is called as the local edge metric dimension of graph �. Here, we analyze the result of local edge metric dimension of some wheel related graph namely fan graph, semi jahangir graph, and jahangir graph