The Wiener index W(G) of a connected graph G is defined as the sum of the distances between all unordered pairs of vertices of G. The eccentricity of a vertex v in G is the distance to a vertex farthest from v. In this paper we obtain the Wiener index of a graph in terms of eccentricities. Further we extend these results to the self-centered graphs.

In a connected graph G, the distance between two vertices of G is length shortest path these vertices. The eccentricity vertex u in largest and any other G. total-eccentricity index ?(G) sum eccentricities all this paper, we find extremal trees, unicyclic bicyclic graphs with respect to index. Moreover, conjugated trees

the paper presents a mathematical base modeling combined to modified-winding -function-approach (mwfa) for eccentricity fault detection of a round-rotor synchronous machine. for this aim, a 6-pole machine is considered, and the machine inductances are computed by mwfa in healthy and also under eccentricity fault. a numerical discrete-time method has been proposed to machine modeling in voltage-...

The adjacent eccentric distance sum index of a graph G is defined as ξsv(G) = ∑ v∈V (G) ε(v)D(v) deg(v) , where ε(v), deg(v) denote the eccentricity, the degree of the vertex v, respectively, and D(v) = ∑ u∈V (G) d(u, v) is the sum of all distances from the vertex v. In this paper we derive some upper or lower bounds for the adjacent eccentric distance sum in terms of some graph invariants or t...

Let G be a connected graph with vertex set V (G) and edge set E(G). The eccentric connectivity index of G, denoted by ξc(G), is defined as ∑ v∈V (G) deg(v)ec(v), where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. In this paper, we propose the edge version of the above index, the edge eccentric connectivity index of G, denoted by ξc e(G), which is defined as ξc e(G) = ∑ f∈E(...

If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.

In angle calibrations the uncertainty contributions of the autocollimator and index table are easily estimated as these uncertainties are well documented, but it is more difficult to determine the uncertainties associated with flatness deviations, eccentricity and pyramidal errors of the measuring faces. Deviations in the flatness of angle surfaces have been held responsible for the lack of agr...

The two-dimensional self-consistent time-dependent theory of beam-wave interaction in gyrotron resonators has been modified to account for eccentricity of the annular hollow electron beam. Numerical analysis yields the effect of beam eccentricity on the previously known limiting values of the azimuthal index of the mode, beyond which stationary single-mode operation becomes impossible. c © 2003...