The super subdivision graph S (G) is obtained from G by replacing every edge e of G by a

complete bipartite graph K2,m (m 2) in such a way that the ends of e are merged with the two vertices of the 2-vertices part of K2,m after removing the edge e from G.

Parisi's famous (proven) conjecture states that the expected cost of an optimal assignment in a

complete bipartite graph on n + n nodes with i.

i] of G by a

complete bipartite graph [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for some [m.

A

complete bipartite graph with [absolute value of U]= [a-z] and [absolute value of V]= [a-z] is denoted by [K.

m,n,] m [less than or equal to] n be a

complete bipartite graph with m + n = p.

2013)), as well as the

complete bipartite graph [K.

For (i), we have k = qt, [lambda] = 0, [mu] = qt, and hence [SIGMA] is the

complete bipartite graph [K.

So we obtain that G is the

complete bipartite graph [K.

Up to now, the spectra are known for some particular graphs: path, cycle, complete graph,

complete bipartite graph, complete tree, hypercube, k-dimensional lattice, star graph, etc.

For example, the 5-cycle is degree-majorized by the

complete bipartite graph K2,3 since (2, 2,2,2,2) is majorized by (2, 2, 2, 3, 3).

Schelp, Path-path Ramsey-type numbers for the

complete bipartite graph, J.

We consider it important to stress the

complete bipartite graph [K.