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.

For a finite connected graph let be the spectral radius of its universal cover. We prove that for any graph of average degree and derive from it the following generalization of the Alon Boppana bound. If the average degree of the graph after deleting any radius ball is at least , then its second largest eigenvalue in absolute value is at least for some absolute constant . This result is tight i...

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.

We analyze the largest eigenvalue and eigenvector for the adjacency matrices of sparse random graph. Let λ1 be the largest eigenvalue of an n-vertex graph, and v1 be its corresponding normalized eigenvector. For graphs of average degree d log n, where d is a large enough constant, we show λ1 = d log n + 1 ± o(1) and 〈1, v1〉 = √ n ( 1−Θ ( 1 logn )) . It shows a limitation of the existing method ...

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....