Generalized stepwise irregular (GSI) graphs are graphs in which the degree difference between every pair of adjacent vertices is positive constant. Specifically, a graph $G $ is called a $ k $-stepwise irregular ( k -SI) graph if $|d_G(u)-d_G(v)|=k$ for each edge $uv \in E(G) $. In this paper, We examine the behavior of GSI graphs under some graph operations, such as sum, corona product, complement, subdivision, line graph, and vertex deletion. An Infinite family of $ 3$-SI graphs with a given cyclomatic number and distinct cycles are constructed. Further, a lower bound on the size of the unicyclic $3$-SI graphs is proposed.
Alizadeh, Y. and Langari, J. (2026). Generalized stepwise irregular graphs: graph operations and construction of $3$-SI graphs. Journal of Discrete Mathematics and Its Applications, 11(1), 33-42. doi: 10.22061/jdma.2025.12410.1156
MLA
Alizadeh, Y. , and Langari, J. . "Generalized stepwise irregular graphs: graph operations and construction of $3$-SI graphs", Journal of Discrete Mathematics and Its Applications, 11, 1, 2026, 33-42. doi: 10.22061/jdma.2025.12410.1156
HARVARD
Alizadeh, Y., Langari, J. (2026). 'Generalized stepwise irregular graphs: graph operations and construction of $3$-SI graphs', Journal of Discrete Mathematics and Its Applications, 11(1), pp. 33-42. doi: 10.22061/jdma.2025.12410.1156
CHICAGO
Y. Alizadeh and J. Langari, "Generalized stepwise irregular graphs: graph operations and construction of $3$-SI graphs," Journal of Discrete Mathematics and Its Applications, 11 1 (2026): 33-42, doi: 10.22061/jdma.2025.12410.1156
VANCOUVER
Alizadeh, Y., Langari, J. Generalized stepwise irregular graphs: graph operations and construction of $3$-SI graphs. Journal of Discrete Mathematics and Its Applications, 2026; 11(1): 33-42. doi: 10.22061/jdma.2025.12410.1156
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