70 research outputs found
A general theorem in spectral extremal graph theory
The extremal graphs and spectral extremal graphs
are the sets of graphs on vertices with
maximum number of edges and maximum spectral radius, respectively, with no
subgraph in . We prove a general theorem which allows us to
characterize the spectral extremal graphs for a wide range of forbidden
families and implies several new and existing results. In
particular, whenever contains the complete
bipartite graph (or certain similar graphs) then
contains the same graph when is sufficiently
large. We prove a similar theorem which relates
and , the set of -free graphs
which maximize the spectral radius of the matrix , where is the adjacency matrix and is the diagonal
degree matrix
- …