The maximum clique problem is a classical problem in combinatorial optimization which
finds important applications in different domains. In this paper we try to give a survey of …

In this paper we present a survey of results concerning algorithms, complexity, and
applications of the maximum clique problem. We discuss enumerative and exact algorithms …

The notion of graph which is most useful in computer science is that of a directed graph or
just a graph. A graph is a combinatorial structure consisting of a finite nonempty set of …

In this paper, it is proved that every triangle-free graph on n≧4 vertices has at most 2^n/2 or
5⋅2^(n-5)/2 independent sets maximal under inclusion, whether n is even or odd. In each …

A subset of vertices is a maximum independent set if no two of the vertices are joined by an
edge and the subset has maximum cardinality. in this paper we answer a question posed by …

A subset of vertices is a maximum independent set if no two of the vertices are adjacent and
the subset has maximum cardinality. A subset of vertices is called a maximum dissociation …

In this paper, we study the problem of determining the largest number of maximum
independent sets of a graph of order n. Solutions to this problem are given for various …

Erdiis and Moser raised the problem of determining the largest number of maximal
independent sets of a general graph of order n and those graphs achieving this maximum …

A maximal independent set of a graph G is an independent set that is not contained properly
in any other independent set of G. In this paper, we determine the maximum number of …

The number of independent vertex subsets is a graph parameter that is, apart from its purely
mathematical importance, of interest in mathematical chemistry. In particular, the problem of …