An edgeipping operation in a triangulation T of a set of points in the plane is a local restructuring that changes T into a triangulation that di ers from T in exactly one edge. The edgeipping distance between two triangulations of the same set of points is the minimum number of edgeipping operations needed to convert one into the other. In the context of computing the rotation distance of bina...

Let G be a simple, undirected graph. We say that two edges of G are within distance 2 of each other if either they are adjacent or there is some other edge that is adjacent to both of them. A distance-2-edge-coloring of G is an assignment of colors to edges so that any two edges within distance 2 of each other have distinct colors, or equivalently, a vertex-coloring of the square of the line gr...

The average distance μ(G) of a connected graph G of order n is the average of the distances between all pairs of vertices of G. We prove that if G is a λ-edge-connected graph of order n, then the bounds μ(G) ≤ 2n/15 + 9, if λ = 5, 6, μ(G) ≤ n/9 + 10, if λ = 7 and μ(G) ≤ n/(λ + 1) + 5, if λ ≥ 8 hold. Our bounds are shown to be best possible and our results solve a problem of Plesńık [12].

The problem of Distance Edge Labeling is a variant of Distance Vertex Labeling (also known as L2,1 labeling) that has been studied for more than twenty years and has many applications, such as frequency assignment. The Distance Edge Labeling problem asks whether the edges of a given graph can be labeled such that the labels of adjacent edges differ by at least two and the labels of edges at dis...

An edge-flipping operation in a triangulation T of a set of points in the plane is a local restructuring that changes T into a triangulation that differs from T in exactly one edge. The edgeflipping distance between two triangulations of the same set of points is the minimum number of edge-flipping operations needed to convert one into the other. In the context of computing the rotation distanc...

A fundamental operation over edge-labeled graphs is the computation of shortest-path distances subject to a constraint on the set of permissible edge labels. Applying exact algorithms for such an operation is not a viable option, especially for massive graphs, or in scenarios where the distance computation is used as a primitive for more complex computations. In this paper we study the problem ...

Face recognition provides broad access to several public devices, so it is essential in the midst of today's technology boom. Human face recognizing has challenge using uncomplicated and straightforward algorithms quickly, memory specifications are not too high, otherwise results quality accurate. combination edge detection Canberra distance can be recommended for applications that require fast...