Browsing by Author "U. Mishra"

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On two-stepwise irregular graphs
(Sharif University of Technology, 2023) S. Das; U. Mishra; S. Rai
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. © 2023 Sharif University of Technology. All rights reserved.