Indexing All Rooted Subgraphs of a Rooted Graph

Tomoki IMADA, Hiroshi NAGAMOCHI

Summary :

Let G be a connected graph in which we designate a vertex or a block (a biconnected component) as the center of G. For each cut-vertex v, let G_v be the connected subgraph induced from G by v and the vertices that will be separated from the center by removal of v, where v is designated as the root of G_v. We consider the set R of all such rooted subgraphs in G, and assign an integer, called an index, to each of the subgraphs so that two rooted subgraphs in R receive the same indices if and only if they are isomorphic under the constraint that their roots correspond each other. In this paper, assuming a procedure for computing a signature of each graph in a class of biconnected graphs, we present a framework for computing indices to all rooted subgraphs of a graph G with a center which is composed of biconnected components from . With this framework, we can find indices to all rooted subgraphs of a outerplanar graph with a center in linear time and space.

• Publication: IEICE TRANSACTIONS on Information Vol.E95-D No.3 pp.712-721
• Publication Date: 2012/03/01
• Online ISSN: 1745-1361
• DOI: 10.1587/transinf.E95.D.712
• Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science – Mathematical Foundations and Applications of Computer Science and Algorithms –)

Authors

Tomoki IMADA
Hiroshi NAGAMOCHI

Keyword

graph isomorphism,  index,  rooted graphs,  outerplanar graphs,  signature