On two-stepwise irregular graphs

Document Type : Article


Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India


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.


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