On the Zagreb indices of overfull molecular graphs

Document Type : Original Article


Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran


Let G be a connected graph on n vertices. An overfull graph is a graph whose number of its edges is greater than Δ × [n/2], where Δ is the maximum degree of vertices in G. In this paper, we compute the Zagreb indices of overfull molecular graphs.

Graphical Abstract

On the Zagreb indices of overfull molecular graphs


[1] G. Chartrand, P. Zhang, Chromatic Graph Theory, Chapman and Hall/CRC, 2008.
[2] A. G. Chetwynd, A. J. W. Hilton, Star multi graphs with three vertices of maximum degree, Math. Proc. Cambr. Phil. Soc. 100 (1986) 303-317.
[3] M. Ghorbani, Remarks of overfull graphs, Applied Mathematics 4 (2013) 1106-1108
[4] I. Gutman, N. Trinajstić, Graph theory and molecular orbitals, Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535 – 538
[5] T. Niessen, How to find overfull subgraphs in graphs with large maximum degree, Disc. Appl. Math. 51 (1994) 117-125.
[6] M. Plantholt, Overfull Conjecture for graphs with high minimum degree, J. Graph Theory 47 (2004) 73-80.
Volume 4, 1-2
June 2014
Pages 37-44
  • Receive Date: 04 January 2014
  • Revise Date: 10 April 2014
  • Accept Date: 10 May 2016
  • Publish Date: 01 June 2014