The annihilation number a of a graph is an upper bound of the independence number α of a graph. In this article we characterize graphs with equal independence and annihilation numbers. In particular, we show that α = a if, and only if, either (1) a ≥ n2 and α ′ = a, or (2) a < n2 and there is a vertex v ∈ V (G) such that α(G − v) = a(G), where α is the critical independence number of the graph....

Suppose G = (V,E) is a simple graph and k is a fixed positive integer. A vertex z k-neighborhood-covers an edge (x, y) if d(z, x) ≤ k and d(z, y) ≤ k. A k-neighborhoodcovering set is a set C of vertices such that every edge in E is k-neighborhood-covered by some vertex in C. A k-neighborhood-independent set is a set of edges in which no two distinct edges can be k-neighborhood-covered by the sa...

This paper describes a method for recognizing real three-dimensional objects in non-controlled backgrounds using independent component analysis to eliminate redundant image information present in each object image. The proposed method is a two-step process that allows a coarse color-based detection and an exact localization using shape information. The paper describes an efficient implementatio...