فهرست نشریات علمی دسترسی آزاد ایران

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.