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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)
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)
—In this paper we propose a graph-based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria. We show that our basic clustering algorithm runs in O(n log n) and with post-processing in O(n 2) (worst case) time where n is the size of the data set. We also show that our generalized(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)