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Journal articles on the topic 'Eccentric vertex'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Deepika, K., K. Suriya, and S. Meenakshi. "ECCENTRIC SEQUENCE OF GRAPHS." Advances in Mathematics: Scientific Journal 9, no. 11 (2020): 9329–33. http://dx.doi.org/10.37418/amsj.9.11.37.

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The minimum length in a graph G between two vertices is defined to be the distance between the two vertices and is denoted by d$\left(a,b\right)$. The farthest vertex distance from a vertex 'a' is known as the eccentricity e(a) of the vertex 'a'. Enumerating the vertex eccentricities in an increasing order is defined as the eccentricity sequence or eccentric sequence of the graph G [11]. The eccentric sequence of some graphs is computed in this paper.

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2

M. K. Angel Jebitha, S. Sujitha, P. Selva Renuka,. "Results on Eccentric Hypergraph of A K-Uniform Tight Cycle." Tuijin Jishu/Journal of Propulsion Technology 44, no. 3 (2023): 1093–97. http://dx.doi.org/10.52783/tjjpt.v44.i3.440.

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Let ℌ be a hypergraph. The eccentric hypergraph ℌ] = of a hypergraph ℌ is the hypergraph that has the same vertex set as in ℌ and the edge set is defined by for any vertex other than x in is an eccentric vertex of x. In this paper we study about some results on eccentric k-uniform tight cycle.

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3

Gamorez, Anabel, and Sergio Canoy Jr. "Monophonic Eccentric Domination Numbers of Graphs." European Journal of Pure and Applied Mathematics 15, no. 2 (2022): 635–45. http://dx.doi.org/10.29020/nybg.ejpam.v15i2.4354.

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Let G be a (simple) undirected graph with vertex and edge sets V (G) and E(G), respectively. A set S ⊆ V (G) is a monophonic eccentric dominating set if every vertex in V (G) \ S has a monophonic eccentric vertex in S. The minimum size of a monophonic eccentric dominating set in G is called the monophonic eccentric domination number of G. It is shown that the absolute difference of the domination number and monophonic eccentric domination number of a graph can be made arbitrarily large. We characterize the monophonic eccentric dominating sets in graphs resulting from the join, corona, and lexi

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4

Akhter, Shehnaz, and Rashid Farooq. "The eccentric adjacency index of unicyclic graphs and trees." Asian-European Journal of Mathematics 13, no. 01 (2018): 2050028. http://dx.doi.org/10.1142/s179355712050028x.

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Let [Formula: see text] be a simple connected graph with vertex set [Formula: see text] and edge set [Formula: see text]. The eccentricity [Formula: see text] of a vertex [Formula: see text] in [Formula: see text] is the largest distance between [Formula: see text] and any other vertex of [Formula: see text]. The eccentric adjacency index (also known as Ediz eccentric connectivity index) of [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the sum of degrees of neighbors of the vertex [Formula: see text]. In this paper, we determine the unicyclic graphs with l

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5

Zhang, Jianbin, and Jianping Li. "On the Maximal Eccentric Distance Sums of Graphs." ISRN Applied Mathematics 2011 (June 14, 2011): 1–9. http://dx.doi.org/10.5402/2011/421456.

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If G is a simple connected graph with vertex V(G), then the eccentric distance sum of G, denoted by ξd(G), is defined as ∑v∈V(G)ecG(v)DG(v), where ecG(v) is the eccentricity of the vertex v and DG(v) is the sum of all distances from the vertex v. Let n≥8. We determine the n-vertex trees with, respectively, the maximum, second-maximum, third-maximum, and fourth-maximum eccentric distance sums. We also characterize the extremal unicyclic graphs on n vertices with respectively, the maximal, second maximal, and third maximal eccentric distance sums.

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6

Kumar, A. Arun, D. Soner Nandappa, and S. R. Nayaka. "THE MINIMUM ECCENTRIC-DOMINATING ENERGY OF A GRAPH." Far East Journal of Mathematical Sciences (FJMS) 141, no. 4 (2024): 327–40. http://dx.doi.org/10.17654/0972087124020.

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Let be a simple graph. A subset of vertices in is said to be an eccentric-dominating set if for each vertex not in , there exists at least one eccentric vertex in and . The cardinality of the minimum eccentric-dominating set is called the eccentric domination number, denoted by . In this article, we define and study the minimum eccentric-dominating energy , and compute the exact value for some standard classes of graphs. Also, we establish some bounds for .

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7

Farahani, Mohammad Reza. "Connective Eccentric Index of an Infinite Family of Linear Polycene Parallelogram Benzenoid." International Letters of Chemistry, Physics and Astronomy 37 (August 2014): 57–62. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.37.57.

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Let G=(V, E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges.We defined dv denote the degree of vertex v∈V(G). The Eccentric Connectivity index ξ(G) and theConnective Eccentric index Cξ(G) of graph G are defined as ξ(G)= ∑ v∈V(G)dv x ξ(v) and Cξ(G)=ξ(G)= ∑ v∈V(G)dv x ξ(v)- where ε(v) is defined as the length of a maximal path connecting a vertex v toanother vertex of G. In this present paper, we compute these Eccentric indices for an infinite family oflinear polycene parallelogram benzenod by a new method.Keywords: Molecular graphs; Linear polycene parallelogra

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8

Farahani, Mohammad Reza. "Connective Eccentric Index of an Infinite Family of Linear Polycene Parallelogram Benzenoid." International Letters of Chemistry, Physics and Astronomy 37 (August 6, 2014): 57–62. http://dx.doi.org/10.56431/p-xgqm51.

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Let G=(V, E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges.We defined dv denote the degree of vertex v∈V(G). The Eccentric Connectivity index ξ(G) and theConnective Eccentric index Cξ(G) of graph G are defined as ξ(G)= ∑ v∈V(G)dv x ξ(v) and Cξ(G)=ξ(G)= ∑ v∈V(G)dv x ξ(v)- where ε(v) is defined as the length of a maximal path connecting a vertex v toanother vertex of G. In this present paper, we compute these Eccentric indices for an infinite family oflinear polycene parallelogram benzenod by a new method.Keywords: Molecular graphs; Linear polycene parallelogra

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9

Naeem, M., M. K. Siddiqui, J. L. G. Guirao, and W. Gao. "New and Modified Eccentric Indices of Octagonal Grid Omn." Applied Mathematics and Nonlinear Sciences 3, no. 1 (2018): 209–28. http://dx.doi.org/10.21042/amns.2018.1.00016.

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AbstractThe eccentricity εu of vertex u in a connected graph G, is the distance between u and a vertex farthermost from u. The aim of the present paper is to introduce new eccentricity based index and eccentricity based polynomial, namely modified augmented eccentric connectivity index and modified augmented eccentric connectivity polynomial respectively. As an application we compute these new indices for octagonal grid $\begin{array}{} \displaystyle O_n^m \end{array}$ and we compare the results obtained with the ones obtained by other indices like Ediz eccentric connectivity index, modified e

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10

Naeem, Muhammad, A. Q. Baig, M. A. Zahid, S. Qaisar, and M. Bari. "ECCENTRIC INDICES OF CRYSTAL CUBIC CARBON STRUCTURE." Latin American Applied Research - An international journal 50, no. 3 (2020): 197–201. http://dx.doi.org/10.52292/j.laar.2020.69.

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Chemical graph theory helps to understand the structural properties of a molecular graph. The molecular graphs are the graphs that consists of atoms called vertices and the covalent bond between them called edges. The eccentricity _u of vertex u in a connected graph G, is the distance between u and a vertex far- thermost from u. In this article, we study the modified eccentric connectivity index _c(G), Ediz eccentric connectivity index E_c(G), Augmented Eccentric Connectivity index A_(G), superaugmented eccentric connectivity index-1, index-2, index-3 and modi_ed eccentric connectivity polynom

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11

Zhang, Xiujun, Muhammad Siddiqui, Muhammad Naeem, and Abdul Baig. "Computing Eccentricity Based Topological Indices of Octagonal Grid Omn." Mathematics 6, no. 9 (2018): 153. http://dx.doi.org/10.3390/math6090153.

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Graph theory is successfully applied in developing a relationship between chemical structure and biological activity. The relationship of two graph invariants, the eccentric connectivity index and the eccentric Zagreb index are investigated with regard to anti-inflammatory activity, for a dataset consisting of 76 pyrazole carboxylic acid hydrazide analogs. The eccentricity ε v of vertex v in a graph G is the distance between v and the vertex furthermost from v in a graph G. The distance between two vertices is the length of a shortest path between those vertices in a graph G. In this paper, we

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12

Bielak, Halina, and Katarzyna Wolska. "On the adjacent eccentric distance sum of graphs." Annales UMCS, Mathematica 68, no. 2 (2014): 1–10. http://dx.doi.org/10.1515/umcsmath-2015-0001.

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AbstractIn this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum. Vol. 7 (2O02) no. 26. 1280-1294].The adjaceni eccentric distance sum index of the graph G is defined aswhere ε(υ) is the eccentricity of the vertex υ, deg(υ) is the degree of the vertex υ and D(υ) = ∑

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13

Nguyen, Kien T., and André Chassein. "Inverse eccentric vertex problem on networks." Central European Journal of Operations Research 23, no. 3 (2014): 687–98. http://dx.doi.org/10.1007/s10100-014-0367-2.

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14

ARISTATIL, Mr A., and Mr M. V. SURESH. "DEGREE-DISTANCE BASED TOPOLOGICAL INDICES OF PRECIOUS STONE CUBIC CARBON STRUCTURE." International Journal of Engineering Technologies and Management Research 6, no. 12 (2020): 101–10. http://dx.doi.org/10.29121/ijetmr.v6.i12.2019.491.

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Chemical diagram hypothesis fathoms the essential properties of a nuclear chart. The sub-nuclear outlines are the charts that are involved particles called vertices and the covalent bond between them are called edges. The unusualness ɛu of vertex u in a related diagram G, is the partition among u and a vertex farthermost from u. In this article, we consider the valuable stone structure of cubic carbon and enrolled Eccentric-network list ξ(G), Eccentric availability polynomial ECP(G, x) and Connective Eccentric list Cξ (G) of pearl structure of cubic carbon for n-levels.

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Mr., A. Aristatil, and M.V. Suresh Mr. "DEGREE-DISTANCE BASED TOPOLOGICAL INDICES OF PRECIOUS STONE CUBIC CARBON STRUCTURE." International Journal of Engineering Technologies and Management Research 6, no. 12 (2020): 101–10. https://doi.org/10.5281/zenodo.3604639.

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Chemical diagram hypothesis fathoms the essential properties of a nuclear chart. The subnuclear outlines are the charts that are involved particles called vertices and the covalent bond between them are called edges. The unusualness ɛu of vertex u in a related diagram G, is the partition among u and a vertex farthermost from u. In this article, we consider the valuable stone structure of cubic carbon and enrolled Eccentric-network list ξ(G), Eccentric availability polynomial ECP (G, x) and Connective Eccentric list Cξ (G) of pearl structure of cubic carbon for n-levels.

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16

Saheli, Mahboubeh, and Ali Reza Ashrafi. "The eccentric connectivity index of armchair polyhex nanotubes." Macedonian Journal of Chemistry and Chemical Engineering 29, no. 1 (2010): 71. http://dx.doi.org/10.20450/mjcce.2010.175.

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The eccentric connectivity index ξ(G) of the graph G is defined as ξ(G) = Σu∈V(G) deg(u)ε(u) where deg(u) denotes the degree of vertex u and ε(u) is the largest distance between u and any other vertex v of G. In this paper an exact expression for the eccentric connectivity index of an armchair polyhex nanotube is given.

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17

Yang, Hong, Muhammad Siddiqui, Misbah Arshad, and Muhammad Naeem. "Degree-Distance Based Topological Indices of Crystal Cubic Carbon Structure." Atoms 6, no. 4 (2018): 62. http://dx.doi.org/10.3390/atoms6040062.

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Chemical graph theory comprehends the basic properties of an atomic graph. The sub-atomic diagrams are the graphs that are comprised of particles called vertices and the covalent bond between them are called edges. The eccentricity ϵ u of vertex u in an associated graph G, is the separation among u and a vertex farthermost from u. In this article, we consider the precious stone structure of cubic carbon and registered Eccentric-connectivity index ξ ( G ) , Eccentric connectivity polynomial E C P ( G , x ) and Connective Eccentric index C ξ ( G ) of gem structure of cubic carbon for n-levels.

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18

Farahani, Mohammad Reza. "Connective Eccentric Index of Circumcoronene Homologous Series of Benzenoid H_k." International Letters of Chemistry, Physics and Astronomy 32 (April 2014): 71–76. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.32.71.

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Let G be a molecular graph, a topological index is a numeric quantity related to G which is invariant under graph automorphisms. The eccentric connectivity index ξ(G) is defined as ξ(G) = ∑vV(G) d x ε(v) where dv, ε(v) denote the degree of vertex v in G and the largest distance between vand any other vertex u of G. The connective eccentric index of graph G is defined as Cξ(G) = ∑vV(G) dv /ε(v) In the present paper we compute the connective eccentric index of CircumcoroneneHomologous Series of Benzenoid Hk (k ≥ 1).

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19

Farahani, Mohammad Reza. "Connective Eccentric Index of Circumcoronene Homologous Series of Benzenoid H<sub>k</sub>." International Letters of Chemistry, Physics and Astronomy 32 (April 22, 2014): 71–76. http://dx.doi.org/10.56431/p-43w6om.

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Let G be a molecular graph, a topological index is a numeric quantity related to G which is invariant under graph automorphisms. The eccentric connectivity index ξ(G) is defined as ξ(G) = ∑vV(G) d x ε(v) where dv, ε(v) denote the degree of vertex v in G and the largest distance between vand any other vertex u of G. The connective eccentric index of graph G is defined as Cξ(G) = ∑vV(G) dv /ε(v) In the present paper we compute the connective eccentric index of CircumcoroneneHomologous Series of Benzenoid Hk (k ≥ 1).

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20

Imran, Muhammad, Abdul Qudair Baig, and Muhammad Razwan Azhar. "The eccentric version of atom-bond connectivity index of tetra sheet networks." Discrete Mathematics, Algorithms and Applications 10, no. 05 (2018): 1850065. http://dx.doi.org/10.1142/s1793830918500659.

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Among topological descriptor of graphs, the connectivity indices are very important and they have a prominent role in theoretical chemistry. The atom-bond connectivity index of a connected graph [Formula: see text] is represented as [Formula: see text], where [Formula: see text] represents the degree of a vertex [Formula: see text] of [Formula: see text] and the eccentric connectivity index of the molecular graph [Formula: see text] is represented as [Formula: see text], where [Formula: see text] is the maximum distance between the vertex [Formula: see text] and any other vertex [Formula: see

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21

Mehdipour, Sara, Mehdi Alaeiyan, and Ali Nejati. "Computing eccentric connectivity index of nanostar dendrimers." Acta Chimica Slovaca 10, no. 2 (2017): 96–100. http://dx.doi.org/10.1515/acs-2017-0017.

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AbstractLet G be a molecular graph, the eccentric connectivity index of G is defined as ξc(G) = Σu∈V(G)deg(u)·ecc(u), where deg(u) denotes the degree of vertex u and ecc(u) is the largest distance between u and any other vertex v of G, namely, eccentricity of u. In this study, we present exact expressions for the eccentric connectivity index of two infinite classes of nanostar dendrimers.

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22

R., Tejaskumar, and A. Mohamed Ismayil. "Bandwagon Distance and Bandwagon Eccentric Domination in Graphs." Asian Research Journal of Mathematics 19, no. 12 (2023): 109–19. http://dx.doi.org/10.9734/arjom/2023/v19i12775.

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In this article, bandwagon distance is introduced and various parameters of bandwagon distance like bandwagon eccentricity, bandwagon eccentric vertex, bandwagon radius, bandwagon diameter, bandwagon center, bandwagon periphery are defined. Bounds on bandwagon radius and bandwagon diameter for class of graphs are found. Bandwagon eccentric domination is defined along with bandwagon eccentric domination number . Necessary and sufficient condition for bandwagon eccentric dominating set is proved. Results related to exact values of bandwagon eccentric domination number of class of graphs is obtai

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23

Aytaç, Aysun, and Belgin Vatansever. "Eccentric connectivity index in transformation graph G^xy+." Acta Universitatis Sapientiae, Informatica 15, no. 1 (2023): 111–23. http://dx.doi.org/10.2478/ausi-2023-0009.

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Abstract Let G be a connected graph with vertex set V(G)and edge set E(G). The eccentric connectivity index of G is defined as ∑ ν ∈ V ( G ) ec ( ν ) deg ( ν ) \sum\limits_{\nu\in{\rm{V}}\left({\rm{G}}\right)}{{\rm{ec}}\left(\nu\right)\,{\rm{deg}}\left(\nu\right)} where ec(v) the eccentricity of a vertex v and deg(v)is its degree and denoted by ɛc(G). In this paper, we investigate the eccentric connectivity index of the transformation graph Gxy+.

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24

Amelia, Risma, Mohammad Nafie Jauhari, and Erna Herawati. "Indeks Konektivitas Eksentrik Edis Pada Graf Annihilator dari Ring Bilangan Bulat Modulo." Jurnal Riset Mahasiswa Matematika 4, no. 3 (2025): 97–109. https://doi.org/10.18860/jrmm.v4i2.30059.

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This study discusses how the general formula of the Ediz eccentric connectivity index (IKEE) in the annihilator graph of the ring of integers modulo. This study aims to determine the Ediz eccentric connectivity index on the annihilator graph of the ring of modular integers , with is a primer number for , and is a positif integer. The initial step in conducting this research is to form an annihilator graph from the ring of integers of the modul , then find the vertex degree and the eccentricity of the vertex on the annihilator graph which is used to calculate the Ediz eccentric connectivity ind

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25

Hasanzadeh, Mehran, Behrooz Alizadeh, Esmaeil Afrashteh, and Fahimeh Baroughi. "Optimal Algorithms for Inverse Eccentric Vertex Location Problem on Extended Star Networks." Asia-Pacific Journal of Operational Research 38, no. 04 (2021): 2150001. http://dx.doi.org/10.1142/s0217595921500019.

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This paper deals with the inverse eccentric vertex location problem on extended star networks in which the aim is to modify the edge lengths at the minimum overall cost within certain modification bounds so that a predetermined vertex becomes the farthest vertex from a given fixed vertex under the new edge lengths. Novel combinatorial algorithms with near-linear time complexities are developed for obtaining the optimal solution of the problem under different cost norms.

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26

Wang, Hongzhuan, and Piaoyang Yin. "On the eccentricity-based invariants of uniform hypergraphs." Filomat 38, no. 1 (2024): 325–42. http://dx.doi.org/10.2298/fil2401325w.

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Let G =(V, E) be a simple connected hypergraph with V the vertex set and E the edge set, respectively. The eccentricity of vertex v refers to the farthest distance of vertex v from other vertices of G, denoted by ?G(v). The eccentric adjacency index (EAI) of G is described as ?ad(G) = ?u?V(G) SG(u)/?G(u), where SG(u) = ? v?NG(u) dG(v). In this work, we consider the gerneralation of the EAI for hypergraphs to draw several conclusions related to extremal problems to EAI. We first propose several bounds on the EAI of k-uniform hypertrees with fixed maximum degree, diameter and edges, respectively

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27

Ghalavand, Ali, Shiladhar Pawar, and Nandappa D. Soner. "Leap Eccentric Connectivity Index of Subdivision Graphs." Journal of Mathematics 2022 (September 19, 2022): 1–7. http://dx.doi.org/10.1155/2022/7880336.

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The second degree of a vertex in a simple graph is defined as the number of its second neighbors. The leap eccentric connectivity index of a graph M , L ξ c M , is the sum of the product of the second degree and the eccentricity of every vertex in M . In this paper, some lower and upper bounds of L ξ c S M in terms of the numbers of vertices and edges, diameter, and the first Zagreb and third leap Zagreb indices are obtained. Also, the exact values of L ξ c S M for some well-known graphs are computed.

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28

Pei, Lidan, and Xiangfeng Pan. "The minimum eccentric distance sum of trees with given distance k-domination number." Discrete Mathematics, Algorithms and Applications 12, no. 04 (2020): 2050052. http://dx.doi.org/10.1142/s1793830920500524.

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Let [Formula: see text] be a positive integer and [Formula: see text] be a simple connected graph. The eccentric distance sum of [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the maximum distance from [Formula: see text] to any other vertex and [Formula: see text] is the sum of all distances from [Formula: see text]. A set [Formula: see text] is a distance [Formula: see text]-dominating set of [Formula: see text] if for every vertex [Formula: see text], [Formula: see text] for some vertex [Formula: see text]. The minimum cardinality among all distance [For

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29

B. M., Abhinaya, Adhithya R., and Tabitha A. M. "Vertex eccentric connectivity index of chemical graphs obtained from (a)bis(pyridine)-cobalt(III)chloride." Acta Universitatis Sapientiae, Informatica 16, no. 1 (2024): 78–104. https://doi.org/10.47745/ausi-2024-0006.

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Let G = (V, E) be a graph. Topological indices are numerical descriptors that provide information about the molecular structure based on the structural properties of the corresponding molecular graph. Among the various topological indices available for graphs, eccentricity-based indices such as vertex eccentric and modified vertex eccentric connectivity indices are particularly significant for QSAR/QSPR studies. In this paper, these indices are computed for self-centered graphs, regular graphs, and graphs obtained by graph operations such as join and Cartesian product. Further, we examine thes

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30

G, Upender Reddy, Siva Nageswara Rao T, Srinivasa Rao N, and Venkateswara Rao V. "Bipolar single valued neutrosophic detour distance." Indian Journal of Science and Technology 14, no. 5 (2021): 427–31. https://doi.org/10.17485/IJST/v14i5.2102.

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Abstract <strong>Objectives:</strong> In the present article, we deduced a characterization of Bipolar Single Valued Neutrosophic (BSVN) radius and eccentricity of the vertex based on Bipolar Single Valued Neutrosophic set(BSVNS) detour. <strong>Method:</strong> We obtained some definitions BSVN on a vertex like BSVN detour eccentric vertex, BSVN detour radius, BSVN detour diameter, BSVN detour centered and BSVN detour periphery. Findings: We derived some important results based on these BSVN detour radius, diameter, center and periphery. <strong>Novelty:</strong> The

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31

Et. al., M. Bhanumathi,. "Eccentric Domination in Boolean Graph BG2(G) of a Graph G." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 9 (2021): 3229–36. http://dx.doi.org/10.17762/turcomat.v12i9.5443.

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Let G be a simple (p, q) graph with vertex set V(G) and edge set E(G). BG2(G) is a graph with vertex set V(G) È E(G) and two vertices are adjacent if and only if they correspond to two adjacent vertices of G, a vertex and an edge incident to it in G or two non-adjacent edges of G. In this paper, we studied eccentric domination number of Boolean graph BG2(G), obtained bounds of this parameter and determined its exact value for several classes of graphs.

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32

Wang, Hongzhuan, Xianhao Shi, and Ber-Lin Yu. "On the eccentric connectivity coindex in graphs." AIMS Mathematics 7, no. 1 (2021): 651–66. http://dx.doi.org/10.3934/math.2022041.

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<abstract><p>The well-studied eccentric connectivity index directly consider the contribution of all edges in a graph. By considering the total eccentricity sum of all non-adjacent vertex, Hua et al. proposed a new topological index, namely, eccentric connectivity coindex of a connected graph. The eccentric connectivity coindex of a connected graph $ G $ is defined as</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \overline{\xi}^{c}(G) = \sum\limits_{uv\notin E(G)} (\varepsilon_{G}(u)+\varepsilon_{G}(v)). $\end{document} </tex-

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Imran, Muhammad, Muhammad Azhar Iqbal, Yun Liu, Abdul Qudair Baig, Waqas Khalid, and Muhammad Asad Zaighum. "Computing Eccentricity-Based Topological Indices of 2-Power Interconnection Networks." Journal of Chemistry 2020 (June 13, 2020): 1–7. http://dx.doi.org/10.1155/2020/3794592.

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In a connected graph G with a vertex v, the eccentricity εv of v is the distance between v and a vertex farthest from v in the graph G. Among eccentricity-based topological indices, the eccentric connectivity index, the total eccentricity index, and the Zagreb index are of vital importance. The eccentric connectivity index of G is defined by ξG = ∑v∈VGdvεv, where dv is the degree of the vertex v and εv is the eccentricity of v in G. The topological structure of an interconnected network can be modeled by using graph explanation as a tool. This fact has been universally accepted and used by com

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Haritha, T., and A. V. Chithra. "On the Distance Spectrum and Distance-Based Topological Indices of Central Vertex-Edge Join of Three Graphs." Armenian Journal of Mathematics 15, no. 10 (2023): 1–16. http://dx.doi.org/10.52737/18291163-2023.15.10-1-16.

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In this paper, we introduce a new graph operation based on a central graph called central vertex-edge join (denoted by $G_{n_1}^C \triangleright (G_{n_2}^V\cup G_{n_3}^E)$) and then determine the distance spectrum of $G_{n_1}^C \triangleright (G_{n_2}^V\cup G_{n_3}^E)$ in terms of the adjacency spectra of regular graphs $G_1$, $G_2$ and $G_3$ when $G_1$ is triangle-free. As a consequence of this result, we construct new families of non-D-cospectral D-equienergetic graphs. Moreover, we determine bounds for the distance spectral radius and distance energy of the central vertex-edge join of three

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Ashrafi, A. R., M. Ghorbani, and M. A. Hossein-Zadeh. "The Eccentric Connectivity Polynomial of some Graph Operations." Serdica Journal of Computing 5, no. 2 (2011): 101–16. http://dx.doi.org/10.55630/sjc.2011.5.101-116.

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The eccentric connectivity index of a graph G, ξ^C, was proposed by Sharma, Goswami and Madan. It is defined as ξ^C(G) = ∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity polynomial is a polynomial version of this topological index. In this paper, exact formulas for the eccentric connectivity polynomial of Cartesian product, symmetric difference, disjunction and join of graphs are presented.

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Latharani, H. M., and D. Soner Nandappa. "ON ve-DEGREE BASED AMPLIFIED ECCENTRIC CONNECTIVITY INDEX OF GRAPHS." Advances and Applications in Discrete Mathematics 42, no. 5 (2025): 465–69. https://doi.org/10.17654/0974165825030.

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Farahani, Mohammad Reza. "Modified Eccentric Connectivity Polynomial of Circumcoronene Series of Benzenoid Hk." JOURNAL OF ADVANCES IN PHYSICS 2, no. 1 (2006): 48–52. http://dx.doi.org/10.24297/jap.v2i1.2102.

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Let G=(V,E) be a molecular graph, where V(G) is a non-empty set of vertices/atoms and E(G) is a set of edges/bonds. For vV(G), defined dv be degree of vertex/atom v and S(v)is the sum of the degrees of its neighborhoods. The modified eccentricity connectivity polynomial of a molecular graph G is defined as Â where Îµ(v) is defined as the length of a maximal path connecting v to another vertex of molecular graph G. In this paper we compute this polynomial for a famous molecular graph of Benzenoid family.

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S, Sowmya. "Eccentric Adjacent Vertex Sum Polynomial of Wheel Related Graphs." International Journal of Mathematics Trends and Technology 65, no. 5 (2019): 27–31. http://dx.doi.org/10.14445/22315373/ijmtt-v65i5p504.

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Devillez, Gauvain, Alain Hertz, Hadrien Mélot, and Pierre Hauweele. "Minimum eccentric connectivity index for graphs with fixed order and fixed number of pendant vertices." Yugoslav Journal of Operations Research 29, no. 2 (2019): 193–202. http://dx.doi.org/10.2298/yjor181115010d.

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The eccentric connectivity index of a connected graph G is the sum over all vertices v of the product dG(v)eG(v), where dG(v) is the degree of v in G and eG(v) is the maximum distance between v and any other vertex of G. We characterize, with a new elegant proof, those graphs which have the smallest eccentric connectivity index among all connected graphs of a given order n. Then, given two integers n and p with p ? n - 1, we characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of order n with p pendant vertices.

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Sorgun, Sezer, and Esma Elyemani. "On the Eccentric Graph of Trees." Ars Combinatoria 159, no. 1 (2024): 87–93. http://dx.doi.org/10.61091/ars159-09.

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We consider the eccentric graph of a graph G , denoted by e c c ( G ) , which has the same vertex set as G , and two vertices in the eccentric graph are adjacent if and only if their distance in G is equal to the eccentricity of one of them. In this paper, we present a fundamental requirement for the isomorphism between e c c ( G ) and the complement of G , and show that the previous necessary condition given in the literature is inadequate. Also, we obtain that the diameter of e c c ( T ) is at most 3 for any tree and get some characterizations of the eccentric graph of trees.

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Yu, Xinhong, Muhammad Imran, Aisha Javed, Muhammad Kamran Jamil, and Xuewu Zuo. "Bounds on the General Eccentric Connectivity Index." Symmetry 14, no. 12 (2022): 2560. http://dx.doi.org/10.3390/sym14122560.

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The general eccentric connectivity index of a graph R is defined as ξec(R)=∑u∈V(G)d(u)ec(u)α, where α is any real number, ec(u) and d(u) represent the eccentricity and the degree of the vertex u in R, respectively. In this paper, some bounds on the general eccentric connectivity index are proposed in terms of graph-theoretic parameters, namely, order, radius, independence number, eccentricity, pendent vertices and cut edges. Moreover, extremal graphs are characterized by these bounds.

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Azari, Mahdieh. "Further results on Zagreb eccentricity coindices." Discrete Mathematics, Algorithms and Applications 12, no. 06 (2020): 2050075. http://dx.doi.org/10.1142/s1793830920500755.

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The eccentric connectivity index and second Zagreb eccentricity index are well-known graph invariants defined as the sums of contributions dependent on the eccentricities of adjacent vertices over all edges of a connected graph. The coindices of these invariants have recently been proposed by considering analogous contributions from the pairs of non-adjacent vertices. Here, we obtain several lower and upper bounds on the eccentric connectivity coindex and second Zagreb eccentricity coindex in terms of some graph parameters such as order, size, number of non-adjacent vertex pairs, radius, and d

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Ahmadini, Abdullah Ali H., Ali N. A. Koam, Ali Ahmad, Martin Bača, and Andrea Semaničová–Feňovčíková. "Computing Vertex-Based Eccentric Topological Descriptors of Zero-Divisor Graph Associated with Commutative Rings." Mathematical Problems in Engineering 2020 (August 24, 2020): 1–6. http://dx.doi.org/10.1155/2020/2056902.

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The applications of finite commutative ring are useful substances in robotics and programmed geometric, communication theory, and cryptography. In this paper, we study the vertex-based eccentric topological indices of a zero-divisor graphs of commutative ring ℤp2×ℤq, where p and q are primes.

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G.Priscilla, Pacifica, and Ajitha J.Jenit. "Steiner µ Distance in Fuzzy Graphs with Application." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 4 (2020): 2156–61. https://doi.org/10.35940/ijeat.D9010.049420.

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In this article we define Steiner and upper Steiner distances in connected fuzzy graphs by combining the notion of Steiner distance with distance and proved that both are metric. Also based on length, eccentricity, radius, diameter, diametric vertex, eccentric vertex, centre, convexity, self-centred graphs are introduced for both Steiner and upper Steiner distances . Some common characteristic properties are analysed and relation between Steiner and upper Steiner distances are discussed with an application. A model result is given for transport network.2010 AMS Classification: 05C72, 05C12

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Ediz, Süleyman. "THE ZAGREB ECCENTRIC VERTEX DEGREE INDICES OF NANOTUBES AND NANOTORI." Advances and Applications in Discrete Mathematics 17, no. 4 (2016): 383–96. http://dx.doi.org/10.17654/dm017040383.

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An, Mingqiang. "On adjacent eccentric distance sum index." Filomat 38, no. 10 (2024): 3639–49. https://doi.org/10.2298/fil2410639a.

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For a connected graph H, the adjacent eccentric distance sum index (AEDSI) is defined assv ?(H)= ?vx?V(H) ?H(xv)?H D (xv)/degH(xv), where ?H (xv)denotes the eccentricity of the vertex vx, degH (xv) is the degree of vx and DH (xv)=?vy?V(H)d(xv,vy) is the sum of all distances from vx in H. AEDSI is proven to be very helpful on predicting anti-HIV activity. In this paper, we give a best possible upper bound on the AEDSI of H with given radius that guarantees H is ?-connected, ?-deficient, ?-Hamiltonian, ?-path-coverable and ?-edge-Hamiltonian, respectively. This supplies a continuation of the res

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Gamorez, Anabel Enriquez, and Sergio R. Canoy Jr. "On a Topological Space Generated by Monophonic Eccentric Neighborhoods of a Graph." European Journal of Pure and Applied Mathematics 14, no. 3 (2021): 695–705. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.3990.

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In this paper, we present a way of constructing a topology on a vertex set of a graph using monophonic eccentric neighborhoods of the graph G.Â In this type of construction, we characterize those graphs that induced the indiscrete topology, the discrete topology, and a particular point topology.

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Hossein-Zadeh, S., A. Hamzeh, and A. R. Ashrafi. "The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs." Serdica Journal of Computing 6, no. 4 (2013): 409–18. http://dx.doi.org/10.55630/sjc.2012.6.409-418.

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Let G1 = (V1, E1) and G2 = (V2, E2) be two graphs having a distinguished or root vertex, labeled 0. The hierarchical product G2 ⊓ G1 of G2 and G1 is a graph with vertex set V2 × V1. Two vertices y2y1 and x2x1 are adjacent if and only if y1x1 ∈ E1 and y2 = x2; or y2x2 ∈ E2 and y1 = x1 = 0. In this paper, the Wiener, eccentric connectivity and Zagreb indices of this new operation of graphs are computed. As an application, these topological indices for a class of alkanes are computed. ACM Computing Classification System (1998): G.2.2, G.2.3.

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Gao, Yun, Li Liang, and Wei Gao. "RESULTS ON GENERALIZED HARARY INDEX AND ECCENTRIC CONNECTIVITY POLYNOMIAL." International Journal of Mathematics and Statistics 1, no. 1 (2015): 1–7. http://dx.doi.org/10.53555/ms.v1i1.1.

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Chemical compounds and drugs are often modeled as graphs where each vertex represents an atom of molecule and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph and can be different structures. In this paper, we determine the accurate formulas to compute the generalized Harary index and eccentric connectivity polynomial of certain special molecular graphs.

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De, Nilanjan, Anita Pal, and Sk Md Abu Nayeem. "Modified Eccentric Connectivity of Generalized Thorn Graphs." International Journal of Computational Mathematics 2014 (December 22, 2014): 1–8. http://dx.doi.org/10.1155/2014/436140.

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The thorn graph GT of a given graph G is obtained by attaching t(>0) pendent vertices to each vertex of G. The pendent edges, called thorns of GT, can be treated as P2 or K2, so that a thorn graph is generalized by replacing P2 by Pm and K2 by Kp and the respective generalizations are denoted by GPm and GKp. The modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighboring vertices, over all vertices of the graph in a hydrogen suppressed molecular structure. In this paper, we give the modified eccentric connectivi

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