The graph isomorphism problem Page 1 128 COMMUNICATIONS OF THE ACM |
NOVEMBER 2020 | VOL. 63 | NO. 11 review articles IMA GE B Y NAD A V/SHUTTERS T …

This book gives an elementary treatment of the basic material about graph spectra, both for
ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering …

Random graph null models have found widespread application in diverse research
communities analyzing network datasets, including social, information, and economic …

In this paper we show that Ω (n) variables are needed for first-order logic with counting to
identify graphs on n vertices. The k-variable language with counting is equivalent to the (k …

'Network'is a heavily overloaded term, so that 'network analysis' means different things to
different people. Specific forms of network analysis are used in the study of diverse …

We announce an algebraic approach to the problem of assigning canonical forms to graphs.
We compute canonical forms and the associated canonical labelings (or renumberings) in …

A program correctness checker is an algorithm for checking the output of a computation.
That is, given a program and an instance on which the program is run, the checker certifies …

Recently, a variety ofresults on the complexitystatusofthegraph isomorphism problem has
been obtained. These results belong to the so-called structural part of Complexity Theory …

An overview of quantum computing and in particular the Hidden Subgroup Problem are
presented from a mathematical viewpoint. Detailed proofs are supplied for many important …

The problem of canonically labeling a graph is studied. Within the general framework of
backtracking algorithms based on individualization and refinement, data structures …