The Irregularity of Some Composite Graphs

Abstract

The irregularity of a simple undirected graph $$G=(V,E)$$ is defined as $$irr(G)=\sum \limits _{uv\in E(G)}|d_G(u)-d_G(v)|$$ , where $$d_G(u)$$ is the degree of the vertex u. This graph invariant is also known as third Zagreb index. In this paper, we investigate how the irregularity of a graph changes with various subdivision operations. Moreover, we find some exact expressions for irregularity of different composite graphs such as double graph, double cover graph, generalized thorn graph and subdivision vertex corona of graphs.