let g be a simple graph. the hosoya polynomial of g is ( , ) ,( , ) = { , } ( ) xd u v h g x  u v v gwhere d(u,v) denotes the distance between vertices u and v . the dendrimer nanostar is apart of a new group of macromolecules. in this paper we compute the hosoya polynomial foran infinite family of dendrimer nanostar. as a consequence we obtain the wiener index andthe hyper-wiener index of th...

Abstract We study the concept of continuous mean distance a weighted graph. For connected unweighted graphs, can be defined as arithmetic distances between all pairs vertices. This parameter provides natural measure compactness graph, and has been intensively studied, together with several variants, including its version for graphs. The analog (discrete) is points on edges Despite being very ge...

Shortest path can be computed in real-time for single navigational instructions. However, complex optimisation tasks, lots of travel-distances (lengths shortest paths) are needed and the total workload becomes a burden. We present fast method estimating travel-distance from one location to another by using an overhead graph that stores ratio between bird-distance few representative locations. T...

As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as $J(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=sumlimits_{vin V}d(u,v)$ is the distance sum of vertex $u$ in $G$, $m$ is the n...