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10.093  Articles
1 of 1.010 pages  |  10  records  |  more records»
The book embedding of a graph G is to arrange the set of points of the graph on a line (spine) and embed the edges on the half-plane bounded by the spine so that the edges in the same page do not intersect with each other. If the maxim... see more

Graph embedding is a powerful method in parallel computing that maps a guest network G into a host network H. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion, and the wirelength. In th... see more

Let G = (V, E) be a simple connected graph. An injective function f : V ? Rn is called an n-dimensional (or n-D) orthogonal labeling of G if uv, uw ? E implies that (f(v) - f(u)) · (f(w) - f(u)) = 0, where · is the usual dot product in Euclidean space. ... see more

The edge-distinguishing chromatic number (EDCN) of a graph G is the minimum positive integer k such that there exists a vertex coloring c : V(G)?{1, 2, …, k} whose induced edge labels {c(u),c(v)} are distinct for al... see more

The QE constant of a finite connected graph G, denoted by QEC(G), is by definition the maximum of the quadratic function associated to the distance matrix on a certain sphere of codimension two. We prove that the QE constants of paths Pn&nb... see more

The matching book embedding of a graph G is to place its vertices on the spine, and arrange its edges on the pages so that the edges in the same page do not intersect each other and the edges induced subgraphs of each page are 1-regular. The mat... see more

A connected graph is said to be of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a graph to be of QE class are derived from the point of vie... see more

A zonal labeling of a plane graph G is an assignment of the two nonzero elements of the ring Z3 of integers modulo 3 to the vertices of G such that the sum of the labels of the vertices on the boundary of each regio... see more

We show that a plane graph can be embedded with its vertices at pre-assigned (fixed) locations in the plane and at most 2.5n+12.5n + 1 bends per edge.  This improves and simplifies a classic result by Pach and Wenger.  The proof extends to grid ... see more

1 of 1.010 pages  |  10  records  |  more records»