Generalized stepwise irregular graphs: graph operations and construction of ۳-SI graphs

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 ۳-SI graphs with a given cyclomatic number and distinct cycles are constructed. Further, a lower bound on the size of the unicyclic ۳-SI graphs is proposed.

کلیدواژه ها:

GSI graph ، \(۳\)-SI graph ، Graph operations ، Cyclomatic number