Energy of unitary Cayley graphs and gcd-graphs
نویسندگان
چکیده
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 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 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 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 areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.
متن کاملEigenspaces of Hamming graphs and unitary Cayley graphs
In this work, the eigenspaces of unitary Cayley graphs and certain Hamming graphs are considered. It is shown that these graph classes are closely related and admit particularly simple eigenspace bases for all eigenvalues, namely bases containing vectors only with entries from the set {0, 1,−1}. A direct consequence is that the considered graph classes are integral.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.03.015