let $g=(v,e)$ be a connected graph. the eccentric connectivity index of $g$, $xi^{c}(g)$, is defined as $xi^{c}(g)=sum_{vin v(g)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. the eccentric distance sum of $g$ is defined as $xi^{d}(g)=sum_{vin v(g)}ec(v)d(v)$, where $d(v)=sum_{uin v(g)}d_{g}(u,v)$ and $d_{g}(u,v)$ is the distance between $u$ and $v$ ...

Expanding parameters of graphs (magnification constant, edge and vertex cutset expansion) are related by very simple inequalities to forwarding parameters (edge and vertex forwarding indices). This shows that certain graphs have eccentricity close to the diameter. Connections between the forwarding indices and algebraic parameters like the smallest eigenvalue of the Laplacian or the genus of th...

In this paper we consider the second eigenfunction of Laplacian with Dirichlet boundary conditions in convex domains. If domain has large eccentricity then exactly two nondegenerate critical points (of course they are one maximum and minimum). The proof uses some estimates proved by Jerison ([13]) Grieser-Jerison ([10]) jointly a topological degree argument. Analogous results for higher order e...

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-...

We consider only finite undirected graphs without loops or multiple edges. Notation and terminology not defined here follow that in [1]. Let G be a graph of order n and size m. We assume that d1, d2, ..., dn, where di, 1 ≤ i ≤ n, is the degree of vertex vi in G, is the degree sequence of G. We define Σk(G) as ∑n i=1 d k i . For each vertex vi, 1 ≤ i ≤ n, mi is defined as the sum of degrees of v...

Abstract We compute the leading coefficient in asymptotic expansion of eigenvalue counting function for Kohn Laplacian on spheres. express as an infinite sum and integral.

For a given graph G, ε(v) and deg(v) denote the eccentricity and the degree of the vertex v in G, respectively. The adjacent eccentric distance sum index of a graph G is defined as [Formula in text], where [Formula in text] is the sum of all distances from the vertex v. In this paper we derive some bounds for the adjacent eccentric distance sum index in terms of some graph parameters, such as i...