In this paper, some results concerning the colorings of graph powers are presented. The notion of helical graphs is introduced. We show that such graphs are hom-universal with respect to high odd-girth graphs whose (2t+1)st power is bounded by a Kneser graph. Also, we consider the problem of existence of homomorphism to odd cycles. We prove that such homomorphism to a (2k+1)cycle exists if and ...

Clustering coefficient is the measure of how tightly vertices are bounded in a network. The Triangle Counting problem is at the core of clustering coefficient computation. We present a new technique for implementing clustering coefficient algorithm on GPUs. It relies on neighbour list being sorted with respect to vertex ID. The algorithm can process very large graphs not seen in the literature ...

The recently introduced concept of k-power domination generalizes domination and power domination, the latter concept being used for monitoring an electric power system. The k-power domination problem is to determine a minimum size vertex subset S of a graph G such that after setting X = N [S], and iteratively adding to X vertices x that have a neighbour v in X such that at most k neighbours of...

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...

Networks play a crucial role in computational biology, yet their analysis and representation is still an open problem. Power Graph Analysis is a lossless transformation of biological networks into a compact, less redundant representation, exploiting the abundance of cliques and bicliques as elementary topological motifs. We demonstrate with five examples the advantages of Power Graph Analysis. ...

The proposed last research entitled "An Effective Data Comparison of Graph Clustering Algorithms via Random Graphs" compared two mostly used algorithms for graph clustering i. e. restricted neighborhood search and markov clustering algorithms via random graph generators i. e. Erdos-Renyi and power law graphs. This paper is an extension to our last research work. In this we have examin...

Graphs possess a strong representational power for many types of patterns. However, a main limitation in their use for pattern analysis derives from their difficult mathematical treatment. One way of circumventing this problem is that of transforming the graphs into a vector space by means of graph embedding. Such an embedding can be conveniently obtained by using a set of ‘‘prototype’’ graphs ...