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On the eccentric distance sum of trees and unicyclic graphs |
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| Authors: | Guihai Yu Lihua Feng |
| Institution: | a School of Mathematics, Shandong Institute of Business and Technology, 191 Binhaizhong Road, Yantai, Shandong, PR China, 264005 b Department of Mathematics, Central South University, Railway Campus, Changsha, Hunan, PR China, 410075 c Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia |
| Abstract: | Let G be a simple connected graph with the vertex set V(G). The eccentric distance sum of G is defined as ξd(G)=∑v∈V(G)ε(v)DG(v), where ε(v) is the eccentricity of the vertex v and DG(v)=∑u∈V(G)d(u,v) is the sum of all distances from the vertex v. In this paper we characterize the extremal unicyclic graphs among n-vertex unicyclic graphs with given girth having the minimal and second minimal eccentric distance sum. In addition, we characterize the extremal trees with given diameter and minimal eccentric distance sum. |
| Keywords: | Eccentricity Eccentric distance sum Unicyclic graph Tree Diameter |
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