Graph Isomorphism SEACM 5.PDF

Classifying pentavalnet symmetric graphs of order $24p$

A graph is said to be symmetric if its automorphism group is transitive on its arcs. A complete classification is given of pentavalent symmetric graphs of order 24p for each prime p. It is shown that a connected pentavalent symmetric graph of order 24p exists if and only if p=2, 3, 5, 11 or 17, and up to isomorphism, there are only eleven such graphs.

Isomorphism classes of cycle permutation graphs

Kwak, J.H. and J. Lee, Isomorphism classes of cycle permutation graphs, Discrete Mathematics 105 (1992) 131-142. In this paper, we construct a cycle permutation graph as a covering graph over the dumbbell graph, and give a new characterization of when two given cycle permutation graphs are isomorphic by a positive or a negative natural isomorphism. Also, we count the isomorphism classes of cycl...

Graph Isomorphism Implementation in LEDA 5 . 1

Graph Isomorphism and the Lasserre Hierarchy

In this paper we show lower bounds for a certain large class of algorithms solving the Graph Isomorphism problem, even on expander graph instances. Spielman [25] shows an algorithm for isomorphism of strongly regular expander graphs that runs in time exp{Õ(n 13 )} (this bound was recently improved to exp{Õ(n 15 )} [5]). It has since been an open question to remove the requirement that the graph...

A Correction to Colbourn's Paper on the Complexity of Matrix Symmetrizability

A square matrix A is transposable ii AT = PAQ for some ljermutation matrices P and Q, and symmiwizable if RA = ( RA)T for some permutation matrix R. A recent paper [I] purports to show that the matrix symmetrizability problem is isomorphism complete, that Is polynomial time equivalent to the graph isomorphism problem. Unfortunately, that paper is based on a misunderstanding about the contents o...