منابع مشابه
Some properties of unitary addition Cayley graphs
Let Γ be an abelian group and B be a subset of Γ. The addition Cayley graph G′ = Cay(Γ, B) is the graph having the vertex set V (G′) = Γ and the edge set E(G′) = {ab : a + b ∈ B}, where a, b ∈ Γ. For a positive integer n > 1, the unitary addition Cayley graph Gn is the graph whose vertex set is Zn, the integers modulo n and if Un denotes set of all units of the ring Zn, then two vertices a, b a...
متن کاملSome Properties of Unitary Cayley Graphs
The unitary Cayley graph Xn has vertex set Zn = {0, 1, . . . , n−1}. Vertices a, b are adjacent, if gcd(a− b, n) = 1. For Xn the chromatic number, the clique number, the independence number, the diameter and the vertex connectivity are determined. We decide on the perfectness of Xn and show that all nonzero eigenvalues of Xn are integers dividing the value φ(n) of the Euler function.
متن کاملExpansion properties of random Cayley graphs and vertex transitive graphs
The Alon-Roichman theorem states that for every ε > 0 there is a constant c(ε), such that the Cayley graph of a finite group G with respect to c(ε) log |G| elements of G, chosen independently and uniformly at random, has expected second largest eigenvalue less than ε. In particular, such a graph is an expander with high probability. Landau and Russell, and independently Loh and Schulman, improv...
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 کاملOn the distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2016
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-016-0699-1