• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.61-74
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• 2021

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.519-524
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• 2007

Facility location problems deal with the concept of centrality and centrality questions are examined using graphs and eccentricity. In this paper, we give interesting properties of a tree in relation with the number of central vertices and peripheral vertices. Also we have some conditions to be an eccentric graph in terms of the girth of a graph.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.487-502
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• 1999

The hydrodynamic flow between two eccentric cylinders is examined for small values of modified Reynolds number porosity parameter and the non-dimensional slip velocity parameter in the presence of a radial magnetic field. The stream function and the pres-sure distribution are calculated and the results are presented graph-ically.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.533-544
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• 2013

The multiplicative version of Wiener index (${\pi}$-index), proposed by Gutman et al. in 2000, is equal to the product of the distances between all pairs of vertices of a (molecular) graph G. In this paper, we first present some sharp bounds in terms of the order and other graph parameters including the diameter, degree sequence, Zagreb indices, Zagreb coindices, eccentric connectivity index and Merrifield-Simmons index for ${\pi}$-index of general connected graphs and trees, as well as a Nordhaus-Gaddum-type bound for ${\pi}$-index of connected triangle-free graphs. Then we study the behavior of ${\pi}$-index upon the case when removing a vertex or an edge from the underlying graph. Finally, we investigate the extremal properties of ${\pi}$-index within the set of trees and unicyclic graphs.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.101-112
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• 2005

In this article, we introduce a generous but eccentric genius in mathematics, Paul Erdos. He invented probabilistic methods, pioneered in their applications to discrete mathematics, and estabilshed new theories, which are regarded as the greatest among his contributions to mathematical world. Here we introduce the probabilistic methods and random graph theory developed by Erdos and look at his life in glance with great respect for him.