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CAYLEY GRAPHS OVER A FINITE CHAIN RING AND GCD-GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  22 January 2016

BORWORN SUNTORNPOCH  and
YOTSANAN MEEMARK
BORWORN SUNTORNPOCH
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok10330, Thailand email [email protected]
YOTSANAN MEEMARK*
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok10330, Thailand email [email protected]
*
✉[email protected]
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Abstract

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We extend spectral graph theory from the integral circulant graphs with prime power order to a Cayley graph over a finite chain ring and determine the spectrum and energy of such graphs. Moreover, we apply the results to obtain the energy of some gcd-graphs on a quotient ring of a unique factorisation domain.

Keywords

energyfinite chain ringsgcd-graphs

MSC classification

Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 3 , June 2016 , pp. 353 - 363
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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