Ramin Javadi

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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 the maximum k for which G has a b-coloring by k colors. It is obvious that χ(G) ≤ φ(G). A graph G is b-continuous if for every k(More)
In this paper, we are interested inminimizing the sum of block sizes in a pairwise balanced design, where there are some constraints on the size of one block or the size of the largest block. For every positive integers n,m, wherem ≤ n, letS (n,m) be the smallest integer s for which there exists a PBD on n points whose largest block has sizem and the sum of(More)
In this paper 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 general(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. In(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)
Flexible job shop scheduling problem (FJSP) is an important extension of the classical job shop scheduling problem, where each operation could be processed on more than one machine and vice versa. Since it has been proven that this problem is strongly NP-hard, it is difficult to achieve an optimal solution with traditional optimization algorithms. In this(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)