@article {
author = {Das, S. and Mishra, U. and Rai, S.},
title = {On two-stepwise irregular graphs},
journal = {Scientia Iranica},
volume = {30},
number = {3},
pages = {1049-1057},
year = {2023},
publisher = {Sharif University of Technology},
issn = {1026-3098},
eissn = {2345-3605},
doi = {10.24200/sci.2022.57725.5388},
abstract = {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.},
keywords = {Irregular Graphs,Bipartite graph,Stepwise irregular graph,Albertson index},
url = {https://scientiairanica.sharif.edu/article_23027.html},
eprint = {https://scientiairanica.sharif.edu/article_23027_5c4981b81459ab6c1945c764de29d4d4.pdf}
}