1 research outputs found
New constructions of non-regular cospectral graphs
We consider two types of joins of graphs and , - the Neighbors Splitting Join and - the
Non Neighbors Splitting Join, and compute the adjacency characteristic
polynomial, the Laplacian characteristic polynomial and the signless Laplacian
characteristic polynomial of these joins. When and are regular,
we compute the adjacency spectrum, the Laplacian spectrum, the signless
Laplacian spectrum of and the normalized
Laplacian spectrum of and .
We use these results to construct non regular, non isomorphic graphs that are
cospectral with respect to the four matrices: adjacency, Laplacian , signless
Laplacian and normalized Laplacian