It is known exactly what periods are possible on certain classes of graphs, such as trees Bitar and Goles (1992), simple cycles Dall'Asta (2006), the complete graph Levine (2008), and the complete bipartite graph
i] of G by a complete bipartite graph [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for some [m.
Vaidya  proved that arbitrary supersubdivision of any tree, grid graph, complete bipartite graph star and [C.
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.
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.
So we obtain that G is the complete bipartite graph
Finally, in Section 5 we give a formula for t(G; 2, -1) when G is a complete bipartite graph
We are going to be looking at a subgraph of the complete bipartite graph
As pointed out in Haglund (2000) the MHH conjecture can be viewed as the analog of the MCP theorem from the complete bipartite graph
We can see that the graph is composed of two complete bipartite graphs
Integrality and Laplacian integrality typically arise from tightly controlled combinatorial structure in special families of graphs, including complete graphs, complete bipartite graphs
and hypercubes (classical; see, e.