Signless Laplacian coefficients and incidence energy of unicyclic graphs with the matching number

摘要

Let Q(G; x) = det (x I - Q(G)) = Sigma(n)(i=0)(-1)(i) phi(i) x(n-i) be the characteristic polynomial of the signless Laplacian matrix Q(G) = D(G) + A(G) of a simple graph G of order n, where D(G) and A(G) are the degree diagonal and adjacency matrices of G, respectively. In this paper, we focus on how the signless Laplacian coefficients of unicyclic graphs change after some graph transformations. These results can be used to characterize all extremal unicyclic graphs having the minimal signless Laplacian coefficients in the set U-(n,U- m) of all unicyclic graphs of order n and the matching number m. Moreover, the unicyclic graphs with minimum incidence energy in U-(n,U- m) are also characterized.