The largest matching root of unicyclic graphs
Let M (G), rho(G) be the largest matching root and the spectral radius of G, respectively. It is well known that M(G) <= rho(G) and the equality holds if and only if G is a tree. In this note, we obtain an upper bound and a lower bound for the largest matching roots of unicyclic graphs and determine the unicyclic graphs which reach those bounds. (C) 2013 Elsevier B.V. All rights reserved.
the largest matching root spectral radius combinatorial problems matching polynomial