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Symmetry 2017, 9(1), 7; doi:10.3390/sym9010007

First and Second Zagreb Eccentricity Indices of Thorny Graphs

1
Department of Mathematics, Government College University Faisalabad, 38000 Faisalabad, Pakistan
2
Department of Applied Chemistry, Government College University Faisalabad, 38000 Faisalabad, Pakistan
3
Department of Mathematics, Government College Women University Faisalabad, 38000 Faisalabad, Pakistan
*
Author to whom correspondence should be addressed.
Academic Editor: Angel Garrido
Received: 21 November 2016 / Revised: 22 December 2016 / Accepted: 22 December 2016 / Published: 6 January 2017
(This article belongs to the Special Issue Symmetry in Complex Networks II)
View Full-Text   |   Download PDF [362 KB, uploaded 6 January 2017]

Abstract

The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let H be a simple graph. The first Zagreb eccentricity index ( E 1 ( H ) ) is defined to be the summation of squares of the eccentricity of vertices, i.e., E 1 ( H ) = u V ( H ) Ɛ H 2 ( u ) . The second Zagreb eccentricity index ( E 2 ( H ) ) is the summation of product of the eccentricities of the adjacent vertices, i.e., E 2 ( H ) = u v E ( H ) Ɛ H ( u ) Ɛ H ( v ) . We obtain the thorny graph of a graph H by attaching thorns i.e., vertices of degree one to every vertex of H . In this paper, we will find closed formulation for the first Zagreb eccentricity index and second Zagreb eccentricity index of different well known classes of thorny graphs. View Full-Text
Keywords: graphs; vertices; complete graph; path; star; cycle graphs; vertices; complete graph; path; star; cycle
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Idrees, N.; Saif, M.J.; Rauf, A.; Mustafa, S. First and Second Zagreb Eccentricity Indices of Thorny Graphs. Symmetry 2017, 9, 7.

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