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CAYLEY GRAPHS OVER A FINITE CHAIN RING AND GCD-GRAPHS

Published online by Cambridge University Press:  22 January 2016

BORWORN SUNTORNPOCH
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok10330, Thailand email beyond.my.limit@gmail.com
YOTSANAN MEEMARK*
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok10330, Thailand email yotsanan.m@chula.ac.th
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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.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Cvetković, D., Doob, M. and Sachs, H., Spectra of Graphs: Theory and Application, 3rd edn, Pure and Applied Mathematics, 87 (Johann Ambrosius Barth, Heidelberg, 1995).Google Scholar
Godsil, C. and Royle, G., Algebraic Graph Theory (Springer, New York, 2001).Google Scholar
Gutman, I., The Energy of a Graph: Old and New Results, Algebraic Combinatorics and Applications (Springer, Berlin, 2001).Google Scholar
Ilić, A., ‘The energy of unitary Cayley graphs’, Linear Algebra Appl. 431 (2009), 18811889.CrossRefGoogle Scholar
Kiani, D., Aghaei, M. M. H., Meemark, Y. and Suntornpoch, B., ‘Energy of unitary Cayley graphs and gcd-graphs’, Linear Algebra Appl. 435(6) (2011), 13361343.Google Scholar
Klotz, W. and Sander, T., ‘Some properties of unitary Cayley graphs’, Electron. J. Combin. 14 (2007), R45, 12 pages.CrossRefGoogle Scholar
Klotz, W. and Sander, T., ‘GCD-graphs and NEPS of complete graphs’, Ars Math. Contemp. 6 (2013), 289299.CrossRefGoogle Scholar
McDonald, B. R., Finite Rings with Identity (Marcel Dekker, New York, 1974).Google Scholar
Norton, G. H. and Sǎlǎgean, A., ‘On the structure of linear and cyclic codes over finite chain rings’, Appl. Algebra Engrg. Comm. Comput. 10(6) (2000), 489506.Google Scholar
Sander, J. W. and Sander, T., ‘The energy of integral circulant graphs with prime power order’, Appl. Anal. Discrete Math. 5 (2011), 2236.CrossRefGoogle Scholar
So, W., ‘Integral circulant graphs’, Discrete Math. 306 (2006), 153158.Google Scholar
West, D. B., Introduction to Graph Theory, 2nd edn (Prentice-Hall, Englewood Cliffs, NJ, 2000).Google Scholar