Sharif University of Technology Scientia Iranica 1026-3098 30 3 2023 06 01 On two-stepwise irregular graphs 1049 1057 23027 10.24200/sci.2022.57725.5388 EN S. Das Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India 0000-0003-0082-6673 U. Mishra Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India S. Rai Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India Journal Article 2021 03 01 A 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