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 کاملComputing Wiener and hyper–Wiener indices of unitary Cayley graphs
The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.
متن کاملOn Unitary Cayley Graphs
AssrRAcr. We deal with a family of undirected Cayley graphs X. which are unions of disjoint Hamilton cycles, and some of their properties, where rz runs over the positive integers. It is proved that X-is a bipartite graph when n is even. If n is an odd number, we count the number of different colored triangles in Xn.
متن کاملSpectral Properties of Unitary Cayley Graphs of Finite Commutative Rings
Let R be a finite commutative ring. The unitary Cayley graph of R, denoted GR, is the graph with vertex set R and edge set {{a, b} : a, b ∈ R, a− b ∈ R×}, where R× is the set of units of R. An r-regular graph is Ramanujan if the absolute value of every eigenvalue of it other than ±r is at most 2 √ r − 1. In this paper we give a necessary and sufficient condition for GR to be Ramanujan, and a ne...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2007
ISSN: 1077-8926
DOI: 10.37236/963