It is commonly believed that vertex-transitive graphs (and in particular Cayley graphs) tend to contain hamilton cycles. The only known connected vertex-transitive graphs without hamilton cycles are K ...

where the sum runs from 0 to [n/2]. It is known that every matching polynomial has only real roots. See [1,2]. It would be interesting to find a vertex transitive graph whose matching polynomial has a ...

Combinatorics and discrete mathematics form a vibrant and expansive branch of modern mathematics, dedicated to the study of finite or countable structures and the methods used to count, classify, and ...