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Maximum Eccentric Connectivity Index for Graphs with Given Diameter [article]

Pierre Hauweele, Alain Hertz, Hadrien Mélot, Bernard Ries and Gauvain Devillez
2018 arXiv   pre-print
Given two integers n and D with D≤ n-1, we characterize those graphs which have the largest eccentric connectivity index among all connected graphs of order n and diameter D.  ...  As a corollary, we also characterize those graphs which have the largest eccentric connectivity index among all connected graphs of a given order n.  ...  The next theorem characterizes the graphs with maximum eccentric connectivity index among those with n ≥ 4 vertices and diameter 2.  ... 
arXiv:1808.10203v1 fatcat:zsdu7vuvnrca3jptggq4f5gbia

Inequalities between degree- and distance-based graph invariants

Imran Nadeem, Hani Shaker
2018 Journal of Inequalities and Applications  
as eccentric connectivity, connective eccentric, augmented eccentric connectivity, Wiener, and third ABC indices.  ...  In this paper we provide a relative study of these classes and derive inequalities between degree-based indices such as Randić connectivity, GA, ABC, and harmonic indices and distance-based indices such  ...  Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.  ... 
doi:10.1186/s13660-018-1633-y pmid:29491690 pmcid:PMC5814576 fatcat:sg2tr64advctzgaqzr6ndu537y

Relationship Between Augmented Eccentric connectivity index and Some Other Graph Invariants

Nilanjan De
2013 International Journal of Advanced Mathematical Sciences  
The augmented eccentric connectivity index of a graph which is a generalization of eccentric connectivity index is defined as the summation of the quotients of the product of adjacent vertex degrees and  ...  In this paper we established some relationships between augmented eccentric connectivity index and several other graph invariants like number of vertices, number of edges, maximum vertex degree, minimum  ...  sharp lower and upper bounds of augmented eccentric connectivity index is given in terms of different graph invariants including the number of vertices (n), number of edges (m), radius (r), diameter (d  ... 
doi:10.14419/ijams.v1i2.701 fatcat:no4pkyvxcrfohklwrxbav76c5a

Eccentric Connectivity Index of Some Special Molecular Graphs and Their R-Corona Graphs

Yun Gao, Li Liang, Wei Gao
2014 International Journal of Chemical and Process Engineering Research  
In this paper, we determine the eccentric connectivity index and augmented eccentric connectivity index of fan graph, wheel graph, gear fan graph, gear wheel graph and their r-corona graphs.  ...  We also would like to thank the anonymous referees for providing us with constructive comments and suggestions.  ...  ACKNOWLEDGEMENTS First, we thank the reviewers for their constructive comments in improving the quality of this paper.  ... 
doi:10.18488/journal.65/2014.1.5/65.5.43.50 fatcat:5shcm3mc3zc6belt5jithpkryy

On eccentric connectivity index [article]

Bo Zhou, Zhibin Du
2010 arXiv   pre-print
We determine the n-vertex trees of diameter with the minimum eccentric connectivity index, and the n-vertex trees of pendent vertices, with the maximum eccentric connectivity index.  ...  We also determine the n-vertex trees with respectively the minimum, second-minimum and third-minimum, and the maximum, second-maximum and third-maximum eccentric connectivity indices for  ...  the maximum, secondmaximum and third-maximum eccentric connectivity indices for n It appears that the eccentric connectivity index satisfies the basic requirement to be a branching index. 6.  ... 
arXiv:1007.2235v1 fatcat:tte4fe2bjjfmddchta35llr6mi

Diametral Reachable Index (DRI) of a Vertex

H. B.Walikar, Shreedevi V. Shindhe
2012 International Journal of Computer Applications  
Every graph has one or more diametral paths. A diametral path of a graph is a shortest path whose length is equal to the diameter of the graph. Let be a diametral vertex.  ...  The total number of diametral paths reachable from a vertex is called the Diametral Reachable Index of that vertex, denoted .  ...  The diametral reachable index of each vertex is given infig 3.(b).Example 2: The diameter of the graph infig. 4(a)is 3. The diametral reachable index of each vertex is given infig 4.(b).  ... 
doi:10.5120/7715-1174 fatcat:zs5d43ebo5ab5okrnqmuw7b6bi

Eccentric Connectivity Index and Polynomial of Some Graphs

A. Bindusree, V. Lokesha, P. Ranjini
2015 British Journal of Mathematics & Computer Science  
Let G be a simple and connected graph with n vertices and m edges. The Eccentric connectivity index of G is defined as the summation of the product of degree and eccentricity of the vertices [15] .  ...  Eccentric connectivity polynomial is a topological polynomial of G which is related to its Eccentric connectivity index [8] .  ...  In addition, the extremal trees with given diameter and minimal eccentric distance sum is also characterized.  ... 
doi:10.9734/bjmcs/2015/15137 fatcat:tuf2wfstnvgijhodi6h3j5f7nq

Eccentric connectivity index [article]

Aleksandar Ilić
2011 arXiv   pre-print
We present the extremal trees and unicyclic graphs with maximum and minimum eccentric connectivity index subject to the certain graph constraints.  ...  Sharp lower and asymptotic upper bound for all graphs are given and various connections with other important graph invariants are established.  ...  I would like to thank Professors Ivan Gutman and Mircea Diudea for their continuous advices and encouragement.  ... 
arXiv:1103.2515v1 fatcat:diyzacypuzc5zbajfjkk7zzefq

On the eccentric connectivity index of a graph

M.J. Morgan, S. Mukwembi, H.C. Swart
2011 Discrete Mathematics  
If G is a connected graph with vertex set V , then the eccentric connectivity index of G, ξ C (G), is defined as is the degree of a vertex v and ec(v) is its eccentricity.  ...  In addition, for trees of given order, when the diameter is also prescribed, precise upper and lower bounds are provided.  ...  The maximum value of the Wiener index, for a graph of given order and diameter, has not been established, but for other parameters, such as the degree distance [3, 10] , Gutman index and the edge-Wiener  ... 
doi:10.1016/j.disc.2009.12.013 fatcat:edqvhkqfdbgrxnt6fvvvdylmwq

On the difference between the eccentric connectivity index and eccentric distance sum of graphs [article]

Yaser Alizadeh, Sandi Klavžar
2020 arXiv   pre-print
The eccentric connectivity index of a graph G is ξ^c(G) = ∑_v ∈ V(G)ε(v)(v), and the eccentric distance sum is ξ^d(G) = ∑_v ∈ V(G)ε(v)D(v), where ε(v) is the eccentricity of v, and D(v) the sum of distances  ...  Sharp lower and upper bounds on ξ^d(G)+ξ^c(G) for arbitrary graphs G are also given, and a sharp lower bound on ξ^d(G) for graphs G with a given radius is proved.  ...  ξ d (G) for graphs G with a given radius.  ... 
arXiv:2005.02635v1 fatcat:infcq3sya5dgvecerv2olw732a

Ordering graphs with large eccentricity-based topological indices

Yunfang Tang, Xuli Qi
2021 Journal of Inequalities and Applications  
AbstractFor a connected graph, the first Zagreb eccentricity index $\xi _{1}$ ξ 1 is defined as the sum of the squares of the eccentricities of all vertices, and the second Zagreb eccentricity index $\  ...  As applications, we obtain and extend some ordering results about the average eccentricity of bicyclic graphs, and the eccentric connectivity index of trees, unicyclic graphs and bicyclic graphs.  ...  Acknowledgements The authors would like to thank the anonymous referees and the editor for very helpful suggestions and comments which led to improvements of the original paper.  ... 
doi:10.1186/s13660-021-02553-7 fatcat:nakqeaztiraezarcbxsggrsoza

On augmented eccentric connectivity index of graphs and trees [article]

Jelena Sedlar
2011 arXiv   pre-print
For graphs that turn out to be extremal explicit formulas for the value of augmented eccentric connectivity index are derived.  ...  In this paper we establish all extremal graphs with respect to augmented eccentric connectivity index among all (simple connected) graphs, among trees and among trees with perfect matching.  ...  As for the augmented eccentric connectivity index, there are some results with explicit formulas for several classes of graphs, in particular for some open and closed unbranched polymers and nanostructure  ... 
arXiv:1107.2272v1 fatcat:perrksqvdjf6llwnsoquifazbm

On the extremal properties of the average eccentricity

Aleksandar Ilić
2012 Computers and Mathematics with Applications  
The average eccentricity is deeply connected with a topological descriptor called the eccentric connectivity index, defined as a sum of products of vertex degrees and eccentricities.  ...  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.  ...  I am grateful to the anonymous referees for their remarks that helped to improve the article and I am indebted to Zhibin Du for several useful suggestions while preparing the article.  ... 
doi:10.1016/j.camwa.2012.04.023 fatcat:zynxb3yjnvbknaw3yacfkt7egy

On the extremal properties of the average eccentricity [article]

Aleksandar Ilic
2011 arXiv   pre-print
The average eccentricity is deeply connected with a topological descriptor called the eccentric connectivity index, defined as a sum of products of vertex degrees and eccentricities.  ...  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.  ...  of trees with given maximum degree Theorem 2.1 Let w be a vertex of a nontrivial connected graph G.  ... 
arXiv:1106.2987v1 fatcat:4ogt7zcwsve7jhm5leud7lepwy

On Reverse Eccentric Connectivity Index of One Tetragonal Carbon Nanocones

Nejati A
2014 Journal of Theoretical and Computational Science  
We have 4 types of vertices for every section of i T . There are 8 vertices of type 1 with maximum eccentric connectivity 4n+2 and S u =5.  ...  In the following theorem, the reverse eccentric connectivity index of C[n] is computed when ( 1) n ≥ is an odd number. Theorem: The reverse eccentric connectivity index of C[n] is given by : ..  ...  Theorem: The reverse eccentric connectivity index of C[n] is given by : is an even number. Proof. With respect to Figure 3 , . We have 4 types of vertices for every section of T i .  ... 
doi:10.4172/2376-130x.1000115 fatcat:ixq3icslxzdzze3txhowfmpnee
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