For a finite connected graph let be the spectral radius of its universal cover. We prove that for any graph of average degree and derive from it the following generalization of the Alon Boppana bound. If the average degree of the graph after deleting any radius ball is at least , then its second largest eigenvalue in absolute value is at least for some absolute constant . This result is tight i...

The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...

Recent research activities have demonstrated the effective application of combinatorial optimization in different areas, especially in software testing. Covering array (CA) has been introduced as a representation of the combinations in one complete set. CAλ(N; t, k, v) is an N × k array in which each t-tuple for an N × t sub array occurs at least λ times, where t is the combination strength, k ...

Proof. The first equality follows directly from (1). To see the second equality, first let M be a matching of size ν(G). For each of the |V | − 2|M | vertices v missed by M , add to M an edge covering v. We obtain an edge cover of size |M |+ (|V | − 2|M |) = |V | − |M |. Hence ρ(G) ≤ |V | − ν(G). Second, let F be an edge cover of size ρ(G). For each v ∈ V delete from F , dF (v) − 1 edges incide...

A Covering Array denoted by CA(N ; t, k, v) is a matrix of size N × k, in which each of the v combinations appears at least once in every t columns. Covering Arrays (CAs) are combinatorial objects used in software testing. There are different methods to construct CAs, but as it is a highly combinatorial problem, few complete algorithms to construct CAs have been reported. In this paper a new ba...