TY - JOUR
ID - 23027
TI - On two-stepwise irregular graphs
JO - Scientia Iranica
JA - SCI
LA - en
SN - 1026-3098
AU - Das, S.
AU - Mishra, U.
AU - Rai, S.
AD - Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India
Y1 - 2023
PY - 2023
VL - 30
IS - 3
SP - 1049
EP - 1057
KW - Irregular Graphs
KW - Bipartite graph
KW - Stepwise irregular graph
KW - Albertson index
DO - 10.24200/sci.2022.57725.5388
N2 - 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.
UR - https://scientiairanica.sharif.edu/article_23027.html
L1 - https://scientiairanica.sharif.edu/article_23027_5c4981b81459ab6c1945c764de29d4d4.pdf
ER -