For a connected graph G and an non-empty set S ⊆ V (G), the Steiner distance dG(S) among the vertices of S is defined as the minimum size among all connected subgraphs whose vertex sets contain S. This concept represents a natural generalization of the concept of classical graph distance. Recently, the Steiner Wiener index of a graph was introduced by replacing the classical graph distance used...

Bankruptcy in the same amount of time and history is very rampant and therefore the vision of the future can be prevented. Using data envelopment analysis (DEA) and malmquist index can precise evaluating of the performances of many different kinds of decision making units (DMU) such as hospitals, universities, business firms, etc. In this paper, we will modify directional distance formulation o...

PURPOSE To compare the tibial tubercle to trochlear groove (TT-TG) distance and index using magnetic resonance imaging (MRI) between children with onetime and recurrent patellar dislocation. METHODS Records of first-time acute patellar dislocations from 2007 to 2012 were reviewed. 20 males and 23 females aged 10 to 17 years at presentation were included for measurements of the bony and cartil...

Three new distance—based topological indices are described; two of them, D and D1 (mean distance topological indices, for any graphs, and for acyclic graphs, respectively) have a modest discriminating ability but may be useful for correlations, e. g. with octane numbers. The third index, J (average distance sum connectivity) is the least degenerate single topological index proposed till now. Th...

the wiener index $w(g)$ of a connected graph $g$‎ ‎is defined as $w(g)=sum_{u,vin v(g)}d_g(u,v)$‎ ‎where $d_g(u,v)$ is the distance between the vertices $u$ and $v$ of‎ ‎$g$‎. ‎for $ssubseteq v(g)$‎, ‎the {it steiner distance/} $d(s)$ of‎ ‎the vertices of $s$ is the minimum size of a connected subgraph of‎ ‎$g$ whose vertex set is $s$‎. ‎the {it $k$-th steiner wiener index/}‎ ‎$sw_k(g)$ of $g$ ...

Perry and Reny (2016) show that the Euclidean length of a citation list satisfies five axioms including "depth relevance". We explore "breadth relevance", which favors consistent achievers over one-hit wonders. A convex combination of depth and breadth relevant citation metrics does not satisfy the independence axiom, but violations are rare. We estimate the parameters of this metric using two ...

The Wiener number W (G) of a graph G is the sum of distances between all pairs of vertices of G. If (G,w) is a vertex-weighted graph, then the Wiener number W (G,w) of (G,w) is the sum, over all pairs of vertices, of products of weights of the vertices and their distance. For G being a partial binary Hamming graph, a formula is given for computing W (G,w) in terms of a binary Hamming labeling o...