A survey of automated conjectures in spectral graph theory

Three conjectures in extremal spectral graph theory

We prove three conjectures regarding the maximization of spectral invariants over certain families of graphs. Our most difficult result is that the join of P2 and Pn−2 is the unique graph of maximum spectral radius over all planar graphs. This was conjectured by Boots and Royle in 1991 and independently by Cao and Vince in 1993. Similarly, we prove a conjecture of Cvetković and Rowlinson from 1...

Beautiful conjectures in graph theory

Spectral Graph Drawing: A Survey

We give an overview of graph drawing techniques as discussed by Godsil/Royle, Koren and Pisanski/Shawe-Taylor. These techniques employ the eigenvectors of the Laplacian matrix to create an n-dimensional representation of an undirected graph.

a survey of translation of metaphors in holy quran – part 20&21

چکیده ندارد.

Spectral graph theory

With every graph (or digraph) one can associate several different matrices. We have already seen the vertex-edge incidence matrix, the Laplacian and the adjacency matrix of a graph. Here we shall concentrate mainly on the adjacency matrix of (undirected) graphs, and also discuss briefly the Laplacian. We shall show that spectral properies (the eigenvalues and eigenvectors) of these matrices pro...