Generalized stepwise irregular (GSI) graphs are graphs in which the degree difference between every pair of adjacent vertices is a positive constant. Specifically, a graph G is called a k-stepwise irregular ( k-SI) graph if |dG(u)-dG(v)|=k for each edge uv∈E(G). In this paper, we examine the behavior of GSI graphs under certain graph operations, including 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 is constructed. Further, a lower bound on the size of the unicyclic 3-SI graphs is proposed.
Langari, J. and Alizadeh, Y. (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
Langari, J. , and Alizadeh, Y. . "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
Langari, J., Alizadeh, Y. (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
J. Langari and Y. Alizadeh, "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
Langari, J., Alizadeh, Y. 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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