On Average Eccentricity of Graphs

Das K. C., Maden A. D., CANGÜL İ. N., ÇEVİK A. S.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, vol.87, no.1, pp.23-30, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 87 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.1007/s40010-016-0315-8
  • Journal Name: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.23-30
  • Keywords: Graph, Distances, Average eccentricity, Eccentricity, Clique number, Independence number, First Zagreb index, Energy, Geometric-arithmetic index (GA1), Atom-bond connectivity index ( ABC), ATOM-BOND CONNECTIVITY, INDEX, ALKANES
  • Bursa Uludag University Affiliated: Yes

Abstract

The eccentricity of a vertex is the maximum distance from it to any other vertex and the average eccentricity avec(G) of a graph G is the mean value of eccentricities of all vertices of G. In this paper we present some lower and upper bounds for the average eccentricity of a connected (molecular) graph in terms of its structural parameters such as number of vertices, diameter, clique number, independence number and the first Zagreb index. Also, we obtain a relation between average eccentricity and first Zagreb index. Moreover, we compare average eccentricity with graph energy, ABC index and index.