Paper Abstract and Keywords |
Presentation |
2016-09-15 10:00
A consideration on complete multipartite graphs that maximize the algebraic connectivity over all graphs with the same number of vertices and edges Ryoya Ishii, Norikazu Takahashi (Okayama Univ.) NLP2016-54 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
The second smallest eigenvalue of the Laplacian matrix of a graph, also known as the algebraic connectivity, is an important measure that represents how strongly the graph is connected. The algebraic connectivity also characterizes the performance of some dynamic processes on networks such as consensus of multiagent networks and synchronization of coupled oscillators. For example, it is well known that the larger the algebraic connectivity of the multiagent network is, the faster the convergence of a representative consensus algorithm. In this report, we consider graphs that maximize the algebraic connectivity over all graphs with the same number of vertices and edges. We first find such graphs with a small number of vertices by using an exhaustive search based on a graph enumeration algorithm. We next focus our attention on the complete multipartite regular graphs, and prove that they maximize the algebraic connectivity over all graphs with the same number of vertices and edges. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
multiagent network / algebraic connectivity / complete multipartite graph / / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 116, no. 215, NLP2016-54, pp. 51-56, Sept. 2016. |
Paper # |
NLP2016-54 |
Date of Issue |
2016-09-07 (NLP) |
ISSN |
Print edition: ISSN 0913-5685 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) |
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NLP2016-54 |
Conference Information |
Committee |
NLP |
Conference Date |
2016-09-14 - 2016-09-15 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Konan Univ. |
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Paper Information |
Registration To |
NLP |
Conference Code |
2016-09-NLP |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
A consideration on complete multipartite graphs that maximize the algebraic connectivity over all graphs with the same number of vertices and edges |
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multiagent network |
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algebraic connectivity |
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complete multipartite graph |
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1st Author's Name |
Ryoya Ishii |
1st Author's Affiliation |
Okayama University (Okayama Univ.) |
2nd Author's Name |
Norikazu Takahashi |
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Okayama University (Okayama Univ.) |
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Speaker |
Author-1 |
Date Time |
2016-09-15 10:00:00 |
Presentation Time |
25 minutes |
Registration for |
NLP |
Paper # |
NLP2016-54 |
Volume (vol) |
vol.116 |
Number (no) |
no.215 |
Page |
pp.51-56 |
#Pages |
6 |
Date of Issue |
2016-09-07 (NLP) |
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