%0 Journal Article
%T On two-stepwise irregular graphs
%J Scientia Iranica
%I Sharif University of Technology
%Z 1026-3098
%A Das, S.
%A Mishra, U.
%A Rai, S.
%D 2023
%\ 06/01/2023
%V 30
%N 3
%P 1049-1057
%! On two-stepwise irregular graphs
%K Irregular Graphs
%K Bipartite graph
%K Stepwise irregular graph
%K Albertson index
%R 10.24200/sci.2022.57725.5388
%X 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.
%U https://scientiairanica.sharif.edu/article_23027_5c4981b81459ab6c1945c764de29d4d4.pdf