Further results regarding the sum of domination number and average eccentricity

Zhibin Du

Applied Mathematics and Computation, 2017, vol. 294, issue C, 299-309

Abstract: The average eccentricity of a graph G, denoted by ecc(G), is the mean value of eccentricities of all vertices of G. Let Dn, i be the n-vertex tree obtained from a path Pn−1=v1v2⋯vn−1 by attaching a pendent vertex to vi. In [13], it was shown that the maximum value for the sum of domination number and average eccentricity among n-vertex (connected) graphs is attained by Dn, 3 when n≡0(mod3), and attained by the path Pn when n¬≡0(mod3). In this paper, we will further determine the second maximum value for the sum of domination number and average eccentricity among n-vertex (connected) graphs. It is interesting that the graphs attaining that second maximum value have three cases, which is Dn, 6 when n≡0(mod3),Dn, 3 when n≡1(mod3), and Tn when n≡2(mod3), where Tn is the n-vertex tree obtained from a path Pn−2=v1v2⋯vn−2 by attaching a pendent vertex to v3, and a pendent vertex to vn−4.

Keywords: Distances; Average eccentricity; Domination number; AGX conjectures (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300316305744
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:294:y:2017:i:c:p:299-309

DOI: 10.1016/j.amc.2016.09.014

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().