ISI-Equienergetic Graphs

The ISI-energy εisi(G) of a graph G=(V,E) is the sum absolute values eigenvalues ISI-matrix C(G)=[cij]n×n in which cij=d(vi)d(vj)d(vi)+d(vj) if vivj∈E(G) and cij=0 otherwise. d(vi) denotes degree vertex vi∈V. As class energy, can be utilized to ascertain general energy conjugated carbon molecules. Two non-isomorphic graphs same order are said ISI-equienergetic their ISI-energies equal. In this paper, we construct pairs connected, ISI-noncospectral, n for all n≥9. addition, n-vertex r(r≥3)-regular G, each k≥2, obtain εisi(Lk(G)¯), depending only on r. This result enables systematic construction ISI-noncospectral order, having equal ISI-energies.