245 research outputs found
Two families of graphs that are Cayley on nonisomorphic groups
A number of authors have studied the question of when a graph can be
represented as a Cayley graph on more than one nonisomorphic group. The work to
date has focussed on a few special situations: when the groups are -groups;
when the groups have order ; when the Cayley graphs are normal; or when the
groups are both abelian. In this paper, we construct two infinite families of
graphs, each of which is Cayley on an abelian group and a nonabelian group.
These families include the smallest examples of such graphs that had not
appeared in other results.Comment: 6 page
A method to determine algebraically integral Cayley digraphs on finite Abelian group
Researchers in the past have studied eigenvalues of Cayley digraphs or
graphs. We are interested in characterizing Cayley digraphs on a finite Abelian
group G whose eigenvalues are algebraic integers in a given number field K. And
we succeed in finding a method to do so by proving Theorem 1. Also, the number
of such Cayley digraphs is computed.Comment: 9 page
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