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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)

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)

This paper is aimed to investigate some computational aspects of different isoperi-metric problems on weighted trees. In this regard, we consider different connectivity parameters called minimum normalized cuts/isoperimteric numbers defined through taking minimum of the maximum or the mean of the normalized outgoing flows from a set of subdomains of… (More)

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