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Paper Abstract and Keywords
Presentation 2023-10-07 13:00
An algorithm for finding regular graphs that maximize algebraic connectivity under a specified number of vertices and degree
Masashi Kurahashi, Tsuyoshi Migita, Norikazu Takahashi (Okayama Univ.) CAS2023-54 NLP2023-53
Abstract (in Japanese) (See Japanese page) 
(in English) Algebraic connectivity is a measure of network robustness, and defined by the second smallest eigenvalue of the Laplacian matrix of the graph. Therefore, finding a graph that maximizes the algebraic connectivity is an important problem in constructing networks that are resilient to attacks and failures. However, even when only the number of vertices and edges are specified, the algebraic connectivity of a graph varies greatly depending on its structure, and the number of graphs satisfying the condition is huge. It is thus difficult to find a graph with the largest algebraic connectivity. In this report, we focus on regular graphs where the degree of all vertices is equal, and consider the problem of finding a regular graph that maximizes the algebraic connectivity under a specified number of vertices and degree. For this problem, we propose a depth-first search algorithm with some pruning techniques, and evaluate its effectiveness experimentally. The proposed algorithm can be used to construct a robust computer network consisting of many switches with the same number of ports.
Keyword (in Japanese) (See Japanese page) 
(in English) algebraic connectivity / Laplacian matrix / regular graphs / depth-first search / pruning / / /  
Reference Info. IEICE Tech. Rep., vol. 123, no. 203, NLP2023-53, pp. 106-110, Oct. 2023.
Paper # NLP2023-53 
Date of Issue 2023-09-29 (CAS, NLP) 
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 CAS2023-54 NLP2023-53

Conference Information
Committee NLP CAS  
Conference Date 2023-10-06 - 2023-10-07 
Place (in Japanese) (See Japanese page) 
Place (in English) Work plaza Gifu 
Topics (in Japanese) (See Japanese page) 
Topics (in English) CAS, NLP, etc. 
Paper Information
Registration To NLP 
Conference Code 2023-10-NLP-CAS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) An algorithm for finding regular graphs that maximize algebraic connectivity under a specified number of vertices and degree 
Sub Title (in English)  
Keyword(1) algebraic connectivity  
Keyword(2) Laplacian matrix  
Keyword(3) regular graphs  
Keyword(4) depth-first search  
Keyword(5) pruning  
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1st Author's Name Masashi Kurahashi  
1st Author's Affiliation Okayama University (Okayama Univ.)
2nd Author's Name Tsuyoshi Migita  
2nd Author's Affiliation Okayama University (Okayama Univ.)
3rd Author's Name Norikazu Takahashi  
3rd Author's Affiliation Okayama University (Okayama Univ.)
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Speaker Author-1 
Date Time 2023-10-07 13:00:00 
Presentation Time 20 minutes 
Registration for NLP 
Paper # CAS2023-54, NLP2023-53 
Volume (vol) vol.123 
Number (no) no.202(CAS), no.203(NLP) 
Page pp.106-110 
#Pages 5 
Date of Issue 2023-09-29 (CAS, NLP) 

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