It is proved that the asymptotic average eccentricity and the asymptotic average degree of both Fibonacci cubes and Lucas cubes are (5 + √ 5)/10 and (5 − √ 5)/5, respectively. A new labeling of the leaves of Fibonacci trees is introduced and it is proved that the eccentricity of a vertex of a given Fibonacci cube is equal to the depth of the associated leaf in the corresponding Fibonacci tree. ...

The Steiner k -eccentricity of a vertex v graph G is the maximum distance over all -subsets V ( ) which contain . In this paper 3-eccentricity studied on trees. Some general properties trees are given. A tree transformation does not increase average As its application, several lower and upper bounds for derived.

Each breast cancer has its unique spatial shape, but the clinical importance and the underlying mechanism for the three-dimensional tumor shapes are mostly unknown. We collected the data on the three-dimensional tumor size and tumor volume data of invasive breast cancers from 2,250 patients who underwent surgery between Jan 2000 and Jul 2007. The degree of tumor eccentricity was estimated by us...

Let G be a connected graph of order n. The eccentricity e(v) vertex v is the distance from to farthest v. average mean all eccentricities in G. We give upper bounds on terms n, minimum degree δ, and girth g. In addition, we construct graphs show that, if for given g there exists Moore δ g, then are asymptotically sharp. Moreover, that can improved large Δ.

In this paper we have classified the nodes of OTIS-cube based on their eccentricities. OTIS (optical transpose interconnection system) is a large scale optoelectronic computer architecture, proposed in [1], that benefit from both optical and electronic technologies. We show that radius and diameter of OTIS-Qn is n + 1 and 2n + 1 respectively. We also show that average eccentricity of OTIS-cube ...

The connective eccentricity index of a graph G is defined as ξce(G) = ∑ v∈V (G) d(v) ε(v) , where ε(v) and d(v) denote the eccentricity and the degree of the vertex v, respectively. In this paper we derive upper or lower bounds for the connective eccentricity index in terms of some graph invariants such as the radius, independence number, vertex connectivity, minimum degree, maximum degree etc....