We give a fully polynomial randomized approximation scheme to compute a lower bound for the matching polynomial of any weighted graph at a positive argument. For the matching polynomial of complete bipartite graphs with bounded weights these lower bounds are asymptotically optimal. 2000 Mathematics Subject Classification: 05A15, 05C70, 15A52, 68Q10.

In this note we give an explanation for two phenomena mentioned in the concluding remarks of " The matching polynomial of a polygraph " by Babic et al. The following results are obtained: (1) Although three matrices for given polygraphs defined in the above article in general have different orders, they determine the same recurrence relations for the matching polynomial of these polygraphs. (2)...

We give a necessary and sufficient condition for the maximum multiplicity of a root of the matching polynomial of a tree to be equal to the minimum number of vertex disjoint paths needed to cover it.

Here we study the normalized Laplacian characteristics polynomial (L-polynomial) for trees and specifically for starlike trees. We describe how the L-polynomial of a tree depends on some topological indices. For which, we also define the higher order general Randić indices for matching and which are different from higher order connectivity indices. Finally we provide the multiplicity of the eig...

In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.

An (N +N) evolutionary algorithm is considered for the problem of finding the maximum cardinality matching in a graph. It is shown that the performance of the evolutionary algorithm is the same as classical simulated annealing. That is, the evolutionary algorithm cannot find the maximum matching in polynomial average time for a family of bipartite graphs considered in this paper although there ...