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Paper Abstract and Keywords
Presentation 2025-12-05 13:30
The linear time algorithm for isomorphism of block cactus graphs
Munetomo Issei, Uehara Ryuhei (JAIST), Nakashima Yuto (Kyudai) COMP2025-16
Abstract (in Japanese) (See Japanese page) 
(in English) The graph isomorphism problem, which determines if two given graphs $G$ and $G'$ are isomorphic, is known to be in the class NP for general graphs.
However, it is unknown whether this problem is NP-complete or solvable in polynomial time.On the other hand, for certain specific graph classes, the graph isomorphism problem is known to be solvable efficiently.
Interval graphs and permutation graphs are examples of such classes.
A common feature of these graph classes is that they can be represented by a tree structure while preserving isomorphism, and it is also known that the graph isomorphism problem for trees can be solved in linear time. This paper studies the isomorphism problem for block cactus graphs.
A block cactus graph is a graph in which all blocks are either cycles or cliques, and these blocks are connected by cut vertices.
Therefore, it can be represented as a tree structure by creating a graph where each block and each cut vertex corresponds to a single vertex.
However, due to partial constraints on vertex ordering, isomorphism cannot be maintained with this representation as-is.
In this paper, we present an algorithm that uses PQ-Trees to solve the isomorphism problem for block cactus graphs with $n$ vertices and $m$ edges in $O(n+m)$ time.
Keyword (in Japanese) (See Japanese page) 
(in English) Block Cactus Graph / Graph Isomorphism / Cycle Graph / Clique Graph / Tree / PQ-Tree / /  
Reference Info. IEICE Tech. Rep., vol. 125, no. 277, COMP2025-16, pp. 17-24, Dec. 2025.
Paper # COMP2025-16 
Date of Issue 2025-11-28 (COMP) 
ISSN Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF COMP2025-16

Conference Information
Committee COMP  
Conference Date 2025-12-05 - 2025-12-05 
Place (in Japanese) (See Japanese page) 
Place (in English) Salon, 2nd Floor, Alumni Hall, Ehime University 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Theoretical Computer Science, etc 
Paper Information
Registration To COMP 
Conference Code 2025-12-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) The linear time algorithm for isomorphism of block cactus graphs 
Sub Title (in English)  
Keyword(1) Block Cactus Graph  
Keyword(2) Graph Isomorphism  
Keyword(3) Cycle Graph  
Keyword(4) Clique Graph  
Keyword(5) Tree  
Keyword(6) PQ-Tree  
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Keyword(8)  
1st Author's Name Munetomo Issei  
1st Author's Affiliation Japan Advanced Institute of Science and Technology (JAIST)
2nd Author's Name Uehara Ryuhei  
2nd Author's Affiliation Japan Advanced Institute of Science and Technology (JAIST)
3rd Author's Name Nakashima Yuto  
3rd Author's Affiliation Kyushu University (Kyudai)
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Speaker Author-1 
Date Time 2025-12-05 13:30:00 
Presentation Time 30 minutes 
Registration for COMP 
Paper # COMP2025-16 
Volume (vol) vol.125 
Number (no) no.277 
Page pp.17-24 
#Pages 8 
Date of Issue 2025-11-28 (COMP) 

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