On Distances between Isomorphism Classes of Graphs

Edge Shift Distance between Trees

Edge shift distance between isomorphism classes of graphs, introduced by M. Johnson, is investigated in the case of trees and compared with other distances .

Distances between graphs under edge operations

We investigate three metrics on the isomorphism classes of graphs derived from elementary edge operations: the edge move, rotation and slide distances. We derive relations between the metrics, and bounds on the distance between arbitrary graphs and between arbitrary trees. We also consider the sensitivity of the metrics to various graph operations. Correspondence to: Wayne Goddard Dept of Compu...

On Isomorphism of Simplicial Complexes and Their Related Algebras

Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs

This paper deals with the graph isomorphism (GI) problem for two graph classes: chordal bipartite graphs and strongly chordal graphs. It is known that GI problem is GI complete even for some special graph classes including regular graphs, bipartite graphs, chordal graphs, comparability graphs, split graphs, and k-trees with unbounded k. On the other side, the relative complexity of the GI probl...

Graph Classes between Parity and Distance-Hereditary Graphs

Several graph problems (e.g., steiner tree, connected domination, hamiltonian path, and isomorphism problem), which can be solved in polynomial time for distance-hereditary graphs, are NP-complete or open for parity graphs. Moreover, the metric characterizations of these two graph classes suggest an excessive gap between them. We introduce a family of classes forming an infinite lattice with re...