A topological index is a function having set of graphs as its domain and real numbers range. Here we concentrated on indices involving the number vertices, edges maximum minimum vertex degree. The aim this paper to compute lower upper bounds second Zagreb index, third Hyper Harmonic Redefined first First reformulated Forgotten square F-index, Sum-connectivity Randic Reciprocal Gourava Sombar Ni...

Let $G$ be a connected graph. The Wiener index of graph is the sum distances between all unordered pairs vertices. We provide asymptotic formulae for maximum simple triangulations and quadrangulations with given connectivity, as order increases, make conjectures extremal based on computational evidence. If $\overline{\sigma}(v)$ denotes arithmetic mean from $v$ to other vertices $G$, then remot...

Let G be a nontrivial connected graph of order n, and k an integer with 2 ≤ k ≤ n. For a set S of k vertices of G, let κ(S) denote the maximum number l of edge-disjoint trees T1, T2, . . . , Tl in G such that V (Ti) ∩ V (Tj) = S for every pair i, j of distinct integers with 1 ≤ i, j ≤ l. Chartrand et al. generalized the concept of connectivity as follows: The k-connectivity, denoted by κk(G), o...

Background: Early diagnosis of patients in the early stages of Alzheimer's, known as mild cognitive impairment, is of great importance in the treatment of this disease. If a patient can be diagnosed at this stage, it is possible to treat or delay Alzheimer's disease. Resting-state functional magnetic resonance imaging (fMRI) is very common in the process of diagnosing Alzheimer's disease. In th...

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 $v$ ...

if we think of the graph as modeling a network, the vulnerability measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. many graph theoretical parameters have been used to describe the vulnerability of communication networks, including connectivity, integrity, toughness, binding number and tenacity.in this paper we discuss...

We propose a simple and natural definition for the Laplacian and the signless Laplacian tensors of a uniform hypergraph. We study their H-eigenvalues, i.e., H-eigenvalues with nonnegative H-eigenvectors, and H-eigenvalues, i.e., H-eigenvalues with positive H-eigenvectors. We show that each of the Laplacian tensor, the signless Laplacian tensor, and the adjacency tensor has at most one H-eigenva...

The partial line digraph technique was introduced in [7] in order to construct digraphs with a minimum diameter, maximum connectivity, and good expandability. To find a new method to construct directed hypergraphs with a minimum diameter, we present in this paper an adaptation of that technique to directed hypergraphs. Directed hypergraphs are used as models for interconnection networks whose v...

We describe a hierarchical volumetric representation of input meshes yielding isocontour output progressively and with decreasing geometric error. The maximum tolerable error bound can be prespeci ed, or incrementally reduced receiving the extra detail in the isosurface with minimal redundancy. We use a hierarchical tetrahedral representation generated via recursive edge-bisections and approxim...