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Generalized stepwise irregular graphs: graph operations and construction of 3-SI graphs | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 11، شماره 1، خرداد 2026، صفحه 33-42 اصل مقاله (420.48 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.12410.1156 | ||
| نویسندگان | ||
| Javaher Langari؛ Yaser Alizadeh* | ||
| Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran. | ||
| تاریخ دریافت: 28 مرداد 1404، تاریخ بازنگری: 20 آبان 1404، تاریخ پذیرش: 24 آبان 1404 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| GSI graph؛ 3-SI graph؛ graph operations؛ cyclomatic number | ||
| مراجع | ||
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