We initiate a systematic study of eigenvectors of random graphs. Whereas much is known about eigenvalues of graphs and how they reflect properties of the underlying graph, relati...
It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by...
Let G = (V + s, E) be a 2-edge-connected graph with a designated vertex s. A pair of edges rs, st is called admissible if splitting off these edges (replacing rs and st by rt) pre...
A graph G is well-covered if every maximal independent set has the same cardinality. Let sk denote the number of independent sets of cardinality k, and define the independence pol...
Free tree, as a special graph which is connected, undirected and acyclic, is extensively used in domains such as computational biology, pattern recognition, computer networks, XML...