• Kyungpook Mathematical Journal
• /
• 제61권1호
• /
• pp.61-74
• /
• 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
• /
• 제25권1_2호
• /
• pp.519-524
• /
• 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
• /
• 제6권2호
• /
• pp.487-502
• /
• 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
• /
• 제31권3_4호
• /
• pp.533-544
• /
• 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.

• 한국수학사학회지
• /
• 제18권4호
• /
• pp.101-112
• /
• 2005

에르디쉬(Erdos)는 수학 연구에 자신의 삶 자체를 모두 바친 20세기를 대표하는 세계적인 수학자이다. 그는 딴은 분야에 걸쳐 1500여 편에 이르는 수학 논문을 발표하였을 뿐만 아니라, 수학의 새로운 지평을 연 영향력 있는 수학자였다. 그는 확률이론을 적용하는 독창적인 방법을 제시하여 확률론적 방법론을 창안하였고, 그러한 방법론은 결국 랜덤 그래프 이론의 모태가 되었다. 본 논문은 천재 수학자, 하지만 다른 한편으로는 바보 같은 순수함을 지녔던 헝가리 출신의 수학자 에르디쉬의 삶을 살퍼보며, 21기에서의 그의 삶과 그의 학문적 업적이 지니는 의미와 가치를 생각하여 보고자 한다.