Synthetic terrain is a key element in many applications that can lessen the sense of realism if it is not handled correctly. We propose a new technique for visualizing terrain surfaces by tessellating them on the GPU. The presented algorithm introduces a new adaptive tessellation scheme for managing the level of detail of the terrain mesh, avoiding the appearance of t-vertices that can produce ...

For a graph, the SK index is equal to half of sum degrees vertices, SK1 product and SK2 square vertices. This paper shows simple unified approach greatest indices for unicyclic graphs by using some transformations characterizes these with first, second, third having order r ≥ 5 girth g 3, where length shortest cycle in graph.

In this paper we establish new inequalities involving Randi$\acute{c}$ index, weigthed index and general in terms of the eigenvalues, number edges, vertices, energy vertex degrees.

Let G be a connected graph. For any two vertices u and v, let d(u, v) denote the distance between u and v in G. The maximum distance between any pair of vertices is called the diameter of G and denoted by diam(G). A radio-labeling (or multi-level distance labeling) with span k for G is a function f that assigns to each vertex with a label from the set {0, 1, 2, · · · , k} such that the followin...

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...

Distance regular graphs fall into three families: primitive, antipodal, and bipar-tite. Each antipodal distance regular graph is a covering graph of a smaller (usually primitive) distance regular graph; the antipodal distance graphs of diameter three are covers of the complete graph, and are the first non-trivial case. Many of the known examples are connected with geometric objects, such as pro...

Distance-hereditary graphs (sensu Howorka) are connected graphs in which all induced paths are isometric. Examples of such graphs are provided by complete multipartite graphs and ptolemaic graphs. Every finite distance-hereditary graph is obtained from K, by iterating the following two operations: adding pendant vertices and splitting vertices. Moreover, distance-hereditary graphs are character...

The center of an F-graph contains at least two vertices, and the distance between any central vertices is equal to radius. In this short note, we describe one way constructing these graphs.