Algebraic Graph Theory: The Matching Polynomial

Talk by Chris Godsil.

A k-matching in a graph is a matching of size k, and p(X,k) denotes the number of k-matchings in X.

The matching polynomial of a graph is a form of generating function for the sequence p(X,k) where k a non-negative integer.

It is closely related to the characteristic polynomial of a graph. I will discuss some of the many interesting properties of this polynomial and some of the related open problems.

[ugashinipreethi]

Sir does matching polynomail exist for graphs with self loops ?

[pavithrajogi]

Sir caan you please explain the theorem called
All zeroes of the matching polynomial of all graphs are real valued.