The geometric origins of spectral graph theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices.

The Ramsey number r ( H ) of a graph ...

Let D(G)=(d"i","j)"n"x"n denote the distance matrix of a connected graph G with order n, where d"i"j is equal to the distance between vertices v"i and v"j in G. The value D"i=@?"j"="1^nd"i"j (i=1,2,...,n) is called the distance degree of vertex v"i. ...