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Academic literature on the topic 'Eccentric vertex'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Eccentric vertex"

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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Books on the topic "Eccentric vertex"

1

McNaughton, Colin. There's an awful lot of weirdos in our neighbourhood: A book of rather silly verse and pictures. Walker Books, 1987.

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2

ill, O'Brien John 1953, ed. Uncle Switch: Loony limericks. McElderry Books, 1997.

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Eccentric, obstinate, and fabulous!: A memoir from Lyngen, Norway to Palos Verdes, California. Donegal Pub. Co., 2008.

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Book chapters on the topic "Eccentric vertex"

1

Gock, E., and K. E. Kurrer. "The eccentric vibratory mill – Innovation of finest grinding." In Mineral Processing on the Verge of the 21st Century. Routledge, 2017. http://dx.doi.org/10.1201/9780203747117-4.

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Bar-Yosef, Eitan. "Eccentric Zion: Victorian Culture and the Jewish Restoration to Palestine." In The Holy Land in English Culture 1799–1917. Oxford University PressOxford, 2005. http://dx.doi.org/10.1093/oso/9780199261161.003.0005.

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Abstract Addressing the members of the Jewish Historical Society of England in 1925, David Lloyd George spoke candidly about the origins of the Balfour Declaration, that short, typed letter dated 2 November 1917, in which ‘one nation solemnly promised to a second nation the country of a third’. ‘It was undoubtedly inspired by natural sympathy, admiration, and also by the fact that, as you must remember, we had been trained even more in Hebrew history than in the history of our own country,’ Lloyd George said: ‘On five days a week in the day school, and on Sunday in our Sunday schools, we were

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