The connection degree index of graphs (original) (raw)

Estimating Graph Robustness Through the Randic Index

IEEE transactions on cybernetics, 2017

Graph robustness--the ability of a graph to preserve its connectivity after the loss of nodes and edges--has been extensively studied to quantify how social, biological, physical, and technical systems withstand to external damages. In this paper, we prove that graph robustness can be quickly estimated through the Randic index, a parameter introduced in chemistry to study organic compounds. We prove that Erdos-Renyj (ER) graphs are a good specimen of robust graphs because they lack of a clear modular structure; we derive an analytical expression for the Randic index of ER graphs and use ER graphs as an effective term of comparison to decide about graph robustness. Experiments on real datasets from different domains (scientific collaboration networks, content-sharing systems, co-purchase networks from an e-commerce platform, and a road network) show that real-life large graphs are more robust than ER ones with the same number of nodes and edges. We also observe that if node degree di...

On Atom-Bond Connectivity Status Index of Graphs

Advances in Mathematics: Scientific Journal

The atom-bond connectivity (ABC) status index of a graph is defined by V. R. Kulli as ABCS(G)= uv∈E(G) (σ u + σ v − 2)/σ u σ v , where σ u is a status of a vertex u ∈ V (G) and is defined as the sum of its distance from every other vertex in V (G). In this paper we have obtained the bounds for the atom-bond connectivity status index. Also obtained atom-bond connectivity status index of some graphs.

Algorithms for the Computation of Communication Network Vulnerability Indexes

A comunication network may be represented as a graph G, where the nodes of the network (hosts, packet switches) and its communication links are modelled as vertices and edges of the graph respectively. The vulnerability of a communication network is de ned as the measurement of the global strength of its underlying graph. The purpose of this paper is to present two vulnerability indexes associated with a graph and the corresponding algorithms, of polynomial time complexity, for computing these functions. The rst vulnerability index we propose is t(G), the number of spanning trees of a graph G. A model extensively used to determine the reliability of a network is the one in which the edges of its underlying graph G survives with equal but independent probability (nodes are perfect). The reliability R(G;) is then de ned as the probability that the surviving edges induce a spanning connected subgraph of G. Let (n; e) represent the class of graphs with n nodes and e edges. Given two graphs G and G 0 which belong to the same class (n; e), if t(G) > t(G 0) then there exist a small value 0 > 0 such that for 0 < 0 ; R(G;) > R(G 0 ;). Thus the number of spanning trees of a graph represents a good measurement of vulnerability. The second vulnerability index of a graph G, here called edge-toughness (G) tell us that in order to split a graph G into k + !(G) components, where !(G) represents the number of connected components of G, we must then remove at least k (G) edges from G, thus (G) measures how tough it is to break up G.

Computing Connection Distance Index of Derived Graphs

Mathematical Problems in Engineering

Distance based topological indices (TIs) play a vital role in the study of various structural and chemical aspects for the molecular graphs. The first distance-based TI is used to find the boiling point of paraffin. The connection distance (CD) index is a latest developed TI that is defined as the sum of all the products of distances between pair of vertices with the sum of their respective connection numbers . In this paper, we computed CD indices of the different derived graphs (subdivision graph S G , vertex-semitotal graph R G , edge-semitotal graph Q G and total graph T G obtained from the graph G under various operations of subdivision in the form of degree distance (DD) and CD indices of the basic graphs including some other algebraic expressions.

The Degree Distance Index for Analysing the Structure of Social Networks

World Academy of Research in Science and Engineering, 2019

Topological indices have been generally used for analyzing the structural properties of graphs and particularly for modeling the biological and the chemical properties of molecules in QSPR and QSAR studies. Recently, these invariants have been proposed as measures to analyze the whole structure of complex networks. In this paper, a new formula for the Degree Distance index using the is obtained. Firstly, we discuss the use of this invariant to analyze the social networks. After that, we apply the new formula on some well-known simple connected graphs, such as Wheels, paths, stars and cycles. Mathematics Subject Classification : 05C12, 05C05

Neighbor Rupture Degree of Some Middle Graphs

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2017

Networks have an important place in our daily lives. Internet networks, electricity networks, water networks, transportation networks, social networks and biological networks are some of the networks we run into every aspects of our lives. A network consists of centers connected by links. A network is represented when centers and connections modelled by vertices and edges, respectively. In consequence of the failure of some centers or connection lines, measurement of the resistance of the network until the communication interrupted is called vulnerability of the network. In this study, neighbor rupture degree which is a parameter that explores the vulnerability values of the resulting graphs due to the failure of some centers of a communication network and its neighboring centers becoming nonfunctional were applied to some middle graphs and neighbor rupture degree of the M(C n), M(P n), M(K 1,n), M(W n), M(P n × K 2) and M(C n × K 2) have been found.

Atom-bond connectivity index of graphs

Discrete Applied Mathematics, 2010

The recently introduced atom-bond connectivity (ABC) index has been applied up until now to study the stability of alkanes and the strain energy of cycloalkanes. Furtula et al. (2009) [3] obtained extremal ABC values for chemical trees, and also, it has been shown that the star K 1,n−1 , has the maximal ABC value of trees. In this paper, we present the lower and upper bounds on ABC index of graphs and trees, and characterize graphs for which these bounds are best possible.

Interrelations of Graph Distance Measures Based on Topological Indices

PLoS ONE, 2014

In this paper, we derive interrelations of graph distance measures by means of inequalities. For this investigation we are using graph distance measures based on topological indices that have not been studied in this context. Specifically, we are using the well-known Wiener index, Randić index, eigenvalue-based quantities and graph entropies. In addition to this analysis, we present results from numerical studies exploring various properties of the measures and aspects of their quality. Our results could find application in chemoinformatics and computational biology where the structural investigation of chemical components and gene networks is currently of great interest.