منابع مشابه
On the Unitary Cayley Signed Graphs
A signed graph (or sigraph in short) is an ordered pair S = (Su, σ), where Su is a graph G = (V,E) and σ : E → {+,−} is a function from the edge set E of Su into the set {+,−}. For a positive integer n > 1, the unitary Cayley graph Xn 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 are adjacent if and only if a...
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 کاملOn the Energy of Unitary Cayley Graphs
In this note we obtain the energy of unitary Cayley graph Xn which extends a result of R. Balakrishnan for power of a prime and also determine when they are hyperenergetic. We also prove that E(Xn) 2(n−1) ≥ 2 4k , where k is the number of distinct prime divisors of n. Thus the ratio E(Xn) 2(n−1) , measuring the degree of hyperenergeticity of Xn, grows exponentially with k.
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 THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS
Let $R$ be a ring (not necessarily commutative) with nonzero identity. We define $Gamma(R)$ to be the graph with vertex set $R$ in which two distinct vertices $x$ and $y$ are adjacent if and only if there exist unit elements $u,v$ of $R$ such that $x+uyv$ is a unit of $R$. In this paper, basic properties of $Gamma(R)$ are studied. We investigate connectivity and the girth of $Gamma(R)$, where $...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/716