Nullity and Energy Bounds of Central Graph of Smith Graphs

A smith graph G is a graph whose at least one eigenvalue is 2. The nullity (G) of a graph G is the multiplicity of the eigenvalue 0 in the spectrum of adjacency matrix of graph A (G). Energy of the graph is the sum of the absolute values of the Eigen values of the adjacency matrix G. Central graph C (G) of graph G is obtained by the subdividing each edge exactly once and joining all the non adjacent vertices of graph G. We have evaluated the nullity and the energy bounds of the central graph of smith graphs. By Huckel molecular Orbital theory, these spectral properties are applicable for determining the stability of unsaturated conjugate hydrocarbons which are isomorphic to central graph of smith graphs.