First and Second Zagreb Eccentricity Indices of Thorny Graphs
Department of Mathematics, Government College University Faisalabad, 38000 Faisalabad, Pakistan
Department of Applied Chemistry, Government College University Faisalabad, 38000 Faisalabad, Pakistan
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
The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let
be a simple graph. The first Zagreb eccentricity index (
) is defined to be the summation of squares of the eccentricity of vertices, i.e.,
. The second Zagreb eccentricity index (
) is the summation of product of the eccentricities of the adjacent vertices, i.e.,
. We obtain the thorny graph of a graph
by attaching thorns i.e., vertices of degree one to every vertex of
. 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.
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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MDPI and ACS Style
Idrees, N.; Saif, M.J.; Rauf, A.; Mustafa, S. First and Second Zagreb Eccentricity Indices of Thorny Graphs. Symmetry 2017, 9, 7.
Idrees N, Saif MJ, Rauf A, Mustafa S. First and Second Zagreb Eccentricity Indices of Thorny Graphs. Symmetry. 2017; 9(1):7.
Idrees, Nazeran; Saif, Muhammad J.; Rauf, Asia; Mustafa, Saba. 2017. "First and Second Zagreb Eccentricity Indices of Thorny Graphs." Symmetry 9, no. 1: 7.
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