Most companies are under heavy time and resource constraints when it comes to testing a software system. Test prioritization technique(s) allows the most useful tests to be executed first, exposing faults earlier in the testing process. Thus makes software testing more efficient and cost effective by covering maximum faults in minimum time. But test case prioritization is not an easy and straig...

In this paper we characterize graphs which maximize the spectral radius of their adjacency matrix over all graphs of Colin de Verdière parameter at most m. We also characterize graphs of maximum spectral radius with no H as a minor when H is either Kr or Ks,t. Interestingly, the extremal graphs match those which maximize the number of edges over all graphs with no H as a minor when r and s are ...

Let G be a random subgraph of the n-cube where each edge appears randomly and independently with small probability p. We prove that the largest eigenvalue of the adjacency matrix of G is almost surely λ1(G) = (1 + o(1))max ( ∆(G), np ) , where ∆(G) is the maximum degree of G and the o(1) term tends to zero as max(∆(G), np) tends to infinity.

We study two-path convexity in bipartite tournaments. For a bipartite tournament, we obtain both a necessary condition and a sufficient condition on the adjacency matrix for its rank to be two. We then investigate 4-cycles in bipartite tournaments of small rank. We show that every vertex in a bipartite tournament of rank two lies on a four cycle, and bipartite tournaments with a maximum number ...

The rank of the adjacency matrix of a graph over the real field is a natural parameter associated with the graph, and there has been substantial interest in relating this to other graph theoretic parameters. In particular the relationship between the rank and chromatic number of a graph, and the rank and the maximum number of vertices of a graph has been extensively studied. This was at least i...

In this paper, it is shown that among connected graphs with maximum clique size ω, the minimum value of the spectral radius of adjacency matrix is attained for a kite graph PKn−ω,ω , which consists of a complete graph Kω to a vertex of which a path Pn−ω is attached. For any fixed ω, a small interval to which the spectral radii of kites PKm,ω , m ≥ 1, belong is exhibited.