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Integral Cayley Graphs Over a Direct Sum of Cyclic Groups of Order 2 and 2p

Usha G. Watson

出版	San Jose State University, 2011
URL	http://books.google.com.hk/books?id=iCluAQAACAAJ&hl=&source=gbs_api

註釋

Cayley graphs for a finite abelian group G are defined over subsets of G called symbols, which are closed under inversion and do not contain the identity element. A symbol S of G is said to be integral if the corresponding Cayley graph has an integral spectrum. We focus on groups of the form Z2 x Z2p, where p is a prime to determine necessary and sufficient conditions for a symbol S to be integral. In preparation, we begin with some basic results from group theory and then give the precise definition of a Cayley graph over G. We then derive a formula for the eigenvalues of a Cayley graph and show how the Boolean algebra generated by the subgroups of G leads to integral symbols. Finally, for groups of the form Z2 x Z2p, we conclude that if S is an integral symbol, then S necessarily lies in the Boolean algebra generated by the subgroups of G.