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RESEARCH PAPERS IN ALGORITHM ANALYSIS
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Provided that the publisher (Algana Associates) and the author(s) remain clearly identified in each and every page, permission is hereby given that the publications below may be produced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise.
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AUTHOR(S) |
TITLE |
DATE |
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DWYER, J.
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CIRCUITS IN COMPLETE GRAPHS AND THEIR RELATIONS TO RAPIDLY-INCREASING SPECIAL FUNCTIONS |
March 2008
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ABSTRACT In graph theory, the number of circuits in a given graph is closely-related to special functions in mathematics, including the Gamma function г(x) and Reciprocal Beta function B-1(x,y). This paper investigates these rapidly-increasing functions and introduces a new function D(x,y), which provides a convenient means of evaluating in a single function the number of Hamilton and Euler circuits in a complete graph Kn. KEYWORDS Algorithm, Beta, Euler, Gamma, Hamilton, graph, function. Acknowledgements: several colleagues and project students contributed to the results detailed in this paper, including Professor Wathek Talebaoui, Danladi Abdulaziz, Karwan Al-Sourchi, Jonathan Arbib, Denka Bancheva, Jordan Berkowitz, Emma Dwyer, Daniel Frincu, Salisu Gambo, Saniul Hossain, Ike Igboanugo, Elyse Loosararian, Alin Petculescu, Vjose Retkoceri, Ademola Shasanya and Long Tran. |
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DWYER, J.
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COUNTING THE NUMBER OF EULER CIRCUITS IN COMPLETE GRAPHS |
April 2008
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ABSTRACT In graph theory, a long standing problem has involved finding a closed form expression for the number of Euler circuits in Kn. The solution presented here comprises a function D(x,y) that has several interesting applications in computing. KEYWORDS Circuit, Development, D function, Euler. Aknowledgements Several colleagues and project students contributed to the results detailed in this paper, including Professor Wathek Talebaoui and Dr Mo Adda at Richmond, The American International University in London (UK), and Professor Brendan McKay at the Australian National University.
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Notes for prospective authors: Please note that the decision of the editorial board of Algana Associates is final in determining the acceptance and publication of a paper in the research papers section.
© Algana Associates 2008 |
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