One of the fundamental properties of a graph is the number of distinct eigenvalues of its adjacency or Laplace matrix. Determining this number is of theoretical interest as well as of practical impact. Sparse graphs with small spectra exhibit excellent structural properties and can act as interconnection topologies. In this paper, for any n we present graphs, for which the product of their vert...

The concept of golden spectral graphs is introduced and some of their general properties reported. Golden spectral graphs are those having a golden proportion for the spectral ratios defined on the basis of the spectral gap, spectral spread and the difference between the second largest and the smallest eigenvalue of the adjacency matrix. They are good expanders and display excellent synchroniza...

So far only one approximation algorithm for the number of perfect matchings in general graphs is known. This algorithm of Chien [2] is based on determinants. We present a much simpler algorithm together with some of its variants. One of them has an excellent performance for random graphs, another one might be a candidate for a good worst case performance. We also present an experimental analysi...

In this paper, a necessary and sufficient condition for the existence of an efficient 2-dominating set in a class of circulant graphs has been obtained and for those circulant graphs, an upper bound for the 2domination number is also obtained. For the circulant graphs Cir(n,A), where A = {1, 2, . . . , x, n − 1, n − 2, . . . , n − x} and x ≤ bn−1 2 c, the perfect 2-tuple total domination number...

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...

let g be a (p, q) graph. let f : v (g) → {1, 2, . . . , k} be a map. for each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of g if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

The notion of graph expansion was introduced as a tool in coding theory by Sipser and Spielman, who used it to bound the minimum distance of a class of low-density codes, as well as the performance of various iterative decoding algorithms for these codes. In spite of its usefulness in establishing theoretical bounds on iterative decoding, graph expansion has not been widely used to design codes...

A number of Cayley-graph interconnection structures, such as cube-connected cycles, butterfly and biswapped networks, are known to be derivable by unified group semidirect product construction. In this paper, we extend these known group semidirect product constructions via a general algebraic construction based on group semidirect product. We show that under certain conditions, graphs based on ...

A set S ⊆ V of vertices in a graph G = (V,E) is called a dominating set if every vertex in V − S is adjacent to at least one vertex in S. Domination in graphs is a well-studied branch of graph theory, and is the subject of two books by Haynes, Hedetniemi and Slater [8, 9]. However, about 90% of the papers on domination have considered only undirected graphs. Thus, relatively little is known abo...

Abstract— In this paper we investigate properties of the Internet topology on the AS (autonomous system) level. Among techniques in spectral graph theory, we find the normalized Laplacian spectrum ( ) of AS graphs 1) unique in spite of the explosive growth of the Internet and 2) distinctive in setting AS graphs apart from synthetic ones. These properties suggest that is an excellent candidate a...