Stepwise Irregular Graphs and Their Metric-Based Resolvability Parameters

Abstract

If the degrees of any two consecutive vertices differ by exactly one, the graph is called a stepwise irregular graph. The study of choosing specific vertices in an ordered subset of the vertex set such that no two vertices have the same representations with regard to the chosen subset is known as resolving parameters. This concept has been expanded for edges as well as a combined version of both. We examine a unique unicyclic stepwise irregular graph and an extended structure of stepwise irregular graph in terms of resolvability parameters to connect the stepwise irregular graph and resolving parameter concepts.