Sharif University of TechnologyScientia Iranica1026-309830320230601On two-stepwise irregular graphs104910572302710.24200/sci.2022.57725.5388ENS. DasDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India0000-0003-0082-6673U. MishraDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, IndiaS. RaiDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, IndiaJournal Article20210301A graph $G$ is called irregular if the degrees of all its vertices are not the same. A graph is said to be \textit{Stepwise Irregular} (SI) if the difference of the degrees of any two adjacent vertices is always 1 (one). This paper deals with \textit{2-Stepwise Irregular} (2-SI) graphs in which the degrees of every pair of adjacent vertices differ by 2. Here we discuss some properties of 2-SI graphs and generalize them for $k$-SI graphs for which the imbalance of every edge is $k$. Besides, we also compute bounds of irregularity for the Albertson index in any 2-SI graph.https://scientiairanica.sharif.edu/article_23027_5c4981b81459ab6c1945c764de29d4d4.pdf