منابع مشابه
Computing 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 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 کاملA Classification of Ramanujan Unitary Cayley Graphs
The unitary Cayley graph on n vertices, Xn, has vertex set Z nZ , and two vertices a and b are connected by an edge if and only if they differ by a multiplicative unit modulo n, i.e. gcd(a− b, n) = 1. A k-regular graph X is Ramanujan if and only if λ(X) 6 2 √ k − 1 where λ(X) is the second largest absolute value of the eigenvalues of the adjacency matrix of X. We obtain a complete characterizat...
متن کاملThe Structure of Unitary Cayley Graphs
In this paper we explore structural properties of unitary Cayley graphs, including clique and chromatic number, vertex and edge connectivity, planarity, and crossing number.
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ژورنال
عنوان ژورنال: Filomat
سال: 2015
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1509079b