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Keywords: b-chromatic number b-coloring Dominating coloring b-continuous graph Kneser graph Steiner triple system a b s t r a c t A b-coloring of a graph G by k colors is a proper k-coloring of G such that in each color class there exists a vertex having neighbors in all the other k − 1 color classes. The b-chromatic number of a graph G, denoted by ϕ(G), is… (More)

A b-coloring of a graph G by k colors is a proper k-coloring of the vertices of G such that in each color class there exists a vertex having neighbors in all the other k − 1 color classes. The b-chromatic number ϕ(G) of a graph G is the maximum k for which G has a b-coloring by k colors. This concept was introduced by R.W. Irving and D.F. Manlove in 1999.… (More)

- Ramin Javadi, Zeinab Maleki, Behanz Omoomi
- 2012

A k−clique covering of a simple graph G, is an edge covering of G by its cliques such that each vertex is contained in at most k cliques. The smallest k for which G admits a k−clique covering is called local clique cover number of G and is denoted by lcc(G). Local clique cover number can be viewed as the local counterpart of the clique cover number which is… (More)

In this paper 2 we consider higher isoperimetric numbers of a (finite directed) graph. In this regard we focus on the nth mean isoperimetric constant of a directed graph as the minimum of the mean outgoing normalized flows from a given set of n disjoint subsets of the vertex set of the graph. We show that the second mean isoperimetric constant in this… (More)

We propose a parallel graph-based data clustering algorithm using CUDA GPU, based on exact clustering of the minimum spanning tree in terms of a minimum isoperi-metric criteria. We also provide a comparative performance analysis of our algorithm with other related ones which demonstrates the general superiority of this parallel algorithm over other… (More)

Given a graph, the sparsest cut problem asks for a subset of vertices whose edge expansion (the normalized cut given by the subset) is minimized. In this paper, we study a generalization of this problem seeking for k disjoint subsets of vertices (clusters) whose all edge expansions are small and furthermore, the number of vertices remained in the exterior… (More)