# Isomorphism for graphs of bounded distance width

Koichi Yamazaki, Hans L. Bodlaender, Babette de Fluiter, Dimitrios M. Thilikos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

## Abstract

In this paper, we study the Graph Isomorphism problem on graphs of bounded treewidth, bounded degree or bounded bandwidth. There are O(n c) algorithms which solve Graph Isomorphism on graphs which have a bound on the treewidth, degree or bandwidth, but the exponent c depends on this bound, where n is the number of vertices in input graphs. We introduce some new graph parameters: the (rooted) path distance width, which is a restriction of bandwidth, and the (rooted) tree distance width, which is a restriction of treewidth. We give algorithms that solve Graph Isomorphism in O(n 2) time for graphs with bounded rooted path distance width, and in O(n 3) time for graphs with bounded rooted tree distance width. Additionally, we show that computing the path distance width of a graph is a NP-complete problem even if the input graphs are restricted to the class of trees. Moreover we show that the rooted path or tree distance width can be computed in O(ne) time and both path and tree distance width can be computed in O(n k+1) time, when they are bounded by a constant k, where e is the number of edges in input graphs. Finally, we study the relationships between the newly introduced parameters and other existing graph parameters.

Original language English (US) Algorithms and Complexity - 3rd Italian Conference, CIAC 1997, Proceedings Giancarlo Bongiovanni, Daniel Pierre Bovet, Giuseppe Di Battista Springer Verlag 276-287 12 3540625925, 9783540625926 https://doi.org/10.1007/3-540-62592-5_79 Published - 1997 3rd Italian Conference on Algorithms and Complexity, CIAC 1997 - Rome, ItalyDuration: Mar 12 1997 → Mar 14 1997

### Publication series

Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 1203 0302-9743 1611-3349

### Other

Other 3rd Italian Conference on Algorithms and Complexity, CIAC 1997 Italy Rome 3/12/97 → 3/14/97

## ASJC Scopus subject areas

• Theoretical Computer Science
• General Computer Science

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