Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...

A rectangular drawing is a partition of a rectangle into a set of rectangles. Rectangular drawings have many important applications including VLSI layout. Since the size of rectangular drawings may be huge, compact encodings are desired. Several compact encodings of rectangular drawings without degree four vertices are known. In this paper, we design two compact encodings for rectangular drawin...

For a given graph G, the square of G, denoted by G2, is a graph with the vertex set V(G) such that two vertices are adjacent if and only if the distance of these vertices in G is at most two. A graph G is called squared if there exists some graph H such that G= H2. A function f:V(G) {0,1,2…, k} is called a coloring of G if for every pair of vertices x,yV(G) with d(x,y)=1 we have |f(x)-f(y)|2 an...

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 ...