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Generalized Stepwise Irregular Graphs: Graph Operations and Construction of $3$-SI Graphs | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 بهمن 1404 اصل مقاله (420.06 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.12410.1156 | ||
| نویسندگان | ||
| Yaser Alizadeh* ؛ Javaher Langari | ||
| 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 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. | ||
| کلیدواژهها | ||
| GSI graph؛ \(3\)-SI graph؛ Graph operations؛ Cyclomatic number | ||
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آمار تعداد مشاهده مقاله: 24 تعداد دریافت فایل اصل مقاله: 13 |
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