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.

We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G, and its Laplacian sum-eccentricity energy LS_eE=sum_{i=1}^n |eta_i|, where eta_i=zeta_i-frac{2m}{n} and where zeta_1,zeta_2,ldots,zeta_n are the eigenvalues of LS_e}. Upper bounds for LS_eE are obtained. A graph is said to be twinenergetic if sum_{i=1}^n |eta_i|=sum_{i=1}^n |zeta_i|. Conditions ...

This report is a review of Darwin’s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equa...

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....