On distance signless Laplacian spectrum of graphs and spectrum of zero divisor graphs of ℤn. Issue 17 (22nd November 2022) - Pirzada, S.; Rather, Bilal A.; Aijaz, M.; Chishti, T. A.
ABSTRACT: For a simple connected graph G of order n, we obtain the distance signless Laplacian spectrum of the joined union of regular graphs G 1, G 2, …, G n in terms of their adjacency spectrum and the spectrum of an auxiliary matrix. As a consequence, we obtain the distance signless Laplacian spectrum of the zero divisor graphs of finite commutative rings Z n for some values of n . We show that Γ ( Z n ) is not in general distance signless Laplacian integral for n = p z, where p is any prime and z ≥ 2. Also, we find the spectrum of Γ ( Z p z ) for certain values of z .