منابع مشابه
Which Cayley Graphs are Integral?
Let G be a non-trivial group, S ⊆ G \ {1} and S = S−1 := {s−1 | s ∈ S}. The Cayley graph of G denoted by Γ(S : G) is a graph with vertex set G and two vertices a and b are adjacent if ab−1 ∈ S. A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine all connected cubic integral Cayley graphs. We also introduce some infinite families of connected integra...
متن کاملIntegral Quartic Cayley Graphs on Abelian Groups
A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine integral quartic Cayley graphs on finite abelian groups. As a side result we show that there are exactly 27 connected integral Cayley graphs up to 11 vertices.
متن کاملIntegral Cayley Graphs over Abelian Groups
Let Γ be a finite, additive group, S ⊆ Γ, 0 6∈ S, − S = {−s : s ∈ S} = S. The undirected Cayley graph Cay(Γ, S) has vertex set Γ and edge set {{a, b} : a, b ∈ Γ, a − b ∈ S}. A graph is called integral, if all of its eigenvalues are integers. For an abelian group Γ we show that Cay(Γ, S) is integral, if S belongs to the Boolean algebra B(Γ) generated by the subgroups of Γ. The converse is proven...
متن کاملCayley graphs - Cayley nets
It is, however, not clear how to choose the generators to produce special graphs. We know many topologies and their generators, but many more may be constructed in the future, having better properties (in terms of diameter, nodal degree and connectivity) than for instance the hypercube. I will present several graphs which connect rings using the generator g 1 and some additional generators.
متن کاملGroups all of whose undirected Cayley graphs are integral
Let G be a finite group, S ⊆ G \ {1} be a set such that if a ∈ S, then a−1 ∈ S, where 1 denotes the identity element of G. The undirected Cayley graph Cay(G, S) ofG over the set S is the graphwhose vertex set is G and two vertices a and b are adjacent whenever ab−1 ∈ S. The adjacency spectrum of a graph is the multiset of all eigenvalues of the adjacency matrix of the graph. A graph is called i...
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ژورنال
عنوان ژورنال: Algebra and Logic
سال: 2019
ISSN: 0002-5232,1573-8302
DOI: 10.1007/s10469-019-09550-2