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

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. ...

##
###
Inequalities between degree- and distance-based graph invariants

2018
*
Journal of Inequalities and Applications
*

as

doi:10.1186/s13660-018-1633-y
pmid:29491690
pmcid:PMC5814576
fatcat:sg2tr64advctzgaqzr6ndu537y
*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. ...##
###
Relationship Between Augmented Eccentric connectivity index and Some Other Graph Invariants

2013
*
International Journal of Advanced Mathematical Sciences
*

The augmented

doi:10.14419/ijams.v1i2.701
fatcat:no4pkyvxcrfohklwrxbav76c5a
*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 ...##
###
Eccentric Connectivity Index of Some Special Molecular Graphs and Their R-Corona Graphs

2014
*
International Journal of Chemical and Process Engineering Research
*

In this paper, we determine the

doi:10.18488/journal.65/2014.1.5/65.5.43.50
fatcat:5shcm3mc3zc6belt5jithpkryy
*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. ...##
###
On eccentric connectivity index
[article]

2010
*
arXiv
*
pre-print

We determine the n-vertex trees of

arXiv:1007.2235v1
fatcat:tte4fe2bjjfmddchta35llr6mi
*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. ...##
###
Diametral Reachable Index (DRI) of a Vertex

2012
*
International Journal of Computer Applications
*

Every

doi:10.5120/7715-1174
fatcat:zs5d43ebo5ab5okrnqmuw7b6bi
*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). ...##
###
Eccentric Connectivity Index and Polynomial of Some Graphs

2015
*
British Journal of Mathematics & Computer Science
*

Let G be a simple and

doi:10.9734/bjmcs/2015/15137
fatcat:tuf2wfstnvgijhodi6h3j5f7nq
*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. ...##
###
Eccentric connectivity index
[article]

2011
*
arXiv
*
pre-print

We present the extremal trees and unicyclic

arXiv:1103.2515v1
fatcat:diyzacypuzc5zbajfjkk7zzefq
*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. ...##
###
On the eccentric connectivity index of a graph

2011
*
Discrete Mathematics
*

If G is a

doi:10.1016/j.disc.2009.12.013
fatcat:edqvhkqfdbgrxnt6fvvvdylmwq
*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 ...##
###
On the difference between the eccentric connectivity index and eccentric distance sum of graphs
[article]

2020
*
arXiv
*
pre-print

The

arXiv:2005.02635v1
fatcat:infcq3sya5dgvecerv2olw732a
*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. ...##
###
Ordering graphs with large eccentricity-based topological indices

2021
*
Journal of Inequalities and Applications
*

AbstractFor a

doi:10.1186/s13660-021-02553-7
fatcat:nakqeaztiraezarcbxsggrsoza
*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. ...##
###
On augmented eccentric connectivity index of graphs and trees
[article]

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 ...

##
###
On the extremal properties of the average eccentricity

2012
*
Computers and Mathematics with Applications
*

The average

doi:10.1016/j.camwa.2012.04.023
fatcat:zynxb3yjnvbknaw3yacfkt7egy
*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. ...##
###
On the extremal properties of the average eccentricity
[article]

2011
*
arXiv
*
pre-print

The average

arXiv:1106.2987v1
fatcat:4ogt7zcwsve7jhm5leud7lepwy
*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. ...##
###
On Reverse Eccentric Connectivity Index of One Tetragonal Carbon Nanocones

2014
*
Journal of Theoretical and Computational Science
*

We have 4 types of vertices

doi:10.4172/2376-130x.1000115
fatcat:ixq3icslxzdzze3txhowfmpnee
*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 . ...
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