Nullity of Corona of a Path with Smith Graphs

Abstract

Let G be a graph and A(G) be its adjacency matrix. The nullity of graph is the presence of zero as an eigenvalue in the spectrum of G. In this paper, we have established the results on nullity of $(P_{n}\odot S_{m})$ where $S_{m}$ is smith graph and $\odot$ is corona product. Moreover we have shown that nullity of $(P_{n}\odot S_{m})$ depends upon the nullity of $S_{m}$, which comes out to be a multiple of nullity of $S_{m}$.