The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity ecc (G) of a graph G is the mean value of eccentricities of all vertices of G. The harmonic index H (G) of a graph G is defined as the sum of 2 di+dj over all edges vivj of G, where di denotes the degree of a vertex vi in G. In this paper, we determine the unique tree with minimum average...

Eccentric distance sum (EDS), which can predict biological and physical properties, is a topological index based on the eccentricity of a graph. In this paper we characterize the chain hexagonal cactus with the minimal and the maximal eccentric distance sum among all chain hexagonal cacti of length n, respectively. Moreover, we present exact formulas for EDS of two types of hexagonal cacti.

The effect of retinal eccentricity on stimulus identification was investigated by measuring observers' ability to identify digits of various sizes presented briefly at different locations in their visual fields. The stimuli were either presented one at a time or presented in pairs with each member of the pair at a different eccentricity and having a different size. Stimulus-response confusion m...

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

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 $v$ ...

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-...

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...

Abstract The eccentricity matrix ? ( G ) of a graph is obtained from the distance by retaining largest distances in each row and column, leaving zeros remaining ones. energy sum absolute values eigenvalues ). Although matrices graphs are closely related to graphs, number properties substantially different those matrices. change due an edge deletion one such property. In this article, we give ex...

The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

Induction motors (IMs) are commonly used in various industrial applications. To improve energy consumption efficiency, a reliable IM health condition monitoring system is very useful to detect IM fault at its earliest stage to prevent operation degradation, and malfunction of IMs. An intelligent harmonic synthesis technique is proposed in this work to conduct incipient air-gap eccentricity faul...