Indexing All Rooted Subgraphs of a Rooted Graph

Tomoki IMADA  Hiroshi NAGAMOCHI  

IEICE TRANSACTIONS on Information and Systems   Vol.E95-D   No.3   pp.712-721
Publication Date: 2012/03/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E95.D.712
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science – Mathematical Foundations and Applications of Computer Science and Algorithms –)
graph isomorphism,  index,  rooted graphs,  outerplanar graphs,  signature,  

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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 Gv 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 Gv. 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.