Let G be a graph with two non adjacent vertices and G0 the graph constructed
from G by adding an edge between them. It is known that the trace of Q0 is 2
plus the trace of Q, where Q and Q0 are the signless Laplacian matrices of G and
G0 respectively. So, the sum of the Q0-eigenvalues of G0 is the sum of the the Q-
eigenvalues of G plus two. It is said that Q-spectral integral variation occurs when
either only one Q-eigenvalue is increased by two or two Q-eigenvalues are increased
by 1 each one. In this article we present some conditions for the occurrence of
Q-spectral integral variation under the addition of an edge to a graph G
