Comparison Between Second Zagreb Eccentricity Index and Eccentric Connectivity Index of Graphs
Journal Title: Current Trends in Computer Sciences & Applications - Year 2018, Vol 1, Issue 1
Abstract
Throughout this paper we only consider the finite, undirected, simple and connected graphs. The degree of v ∊ V(G), denoted by degG(v), is the number of vertices in G adjacent to v. For any two vertices u; v in a graph G, the distance between them, denoted by (,) G d uv is the length of a shortest path connecting them in G. As usual, let Sn, Pn, Cn, Kn be the star graph, path graph, cycle graph and complete graph, respectively, on n vertices. Other undefined notations and terminology on the graph theory can be found in [1]. For any vertex of graph G, the eccentricity ( ) G ε v (or ε ( ) v for short) is the maximum distance from v to other vertices of G, i.e., ( ) G ε v = maxu≠v (,) G d uv . The eccentricity of a vertex is an important parameter in pure graph theory. The radius of a graph G is denoted by r(G) and defined by r = r(G) = {minε ( ) v | v ∈ V(G)}. Also, the diameter of G, denoted by d(G), is the maximum distance between vertices of a graph G and hence d = d(G) = max{ ε ( ) v | v ∈ V(G)}. A vertex v with ( ) G ε v = r(G) is called a central vertex in G. A graph G with d(G) = r(G) is called a self-centered graph. A graph which contains only two non-central vertices is called almost self-centered graph [2] (ASC graph for short). Moreover, the eccentricity is also applied in chemical graph theory.
Authors and Affiliations
Huimin Li, Fang Gao, Kexiang Xu
Keywords
Related Articles
- EP ID EP587426
- DOI -
- Views 76
- Downloads 0
Mini View on Current Trends in Computer Sciences & Applications
Computer science has contributed a lot for making the life of human being smooth. The recent developments in the field of computer science are proven to be more smarter and more applicable structures result from marrying...
Self-Payment Fraud Detection on Automated Teller Machine
Over the past decade the amount of transactions and reported frauds on Automated Teller Machines (ATM) has significantly increased. Various types of frauds have been reported around misusing ATM cards and many methods ha...
Mitigating Disaster using Secure Threshold-Cloud Architecture
There are many risks in moving data into public cloud environments, along with an increasing threat around large-scale data leakage during cloud outages. This work aims to apply secret sharing methods as used in cryptogr...
In Pursuit of Privacy: An Introduction to Anonymization Technologies
Privacy in the age of pervasive computing and networking is a very hard topic to fully grasp. Any serious attempt at discussing it must take many different angles into account. User interactions grow richer month after m...
An Image Secret Sharing Method Based on Shamir Secret Sharing
This paper presents an image secret sharing method based on Shamir secret sharing method. We use the matrix projection to construct secret sharing scheme. A secret image to be divided as n image shares such that: i) Any...