IJPAM: Volume 86, No. 6 (2013)


Antony Xavier$^{1}$, A.S. Shanthi$^{2}$, Maria Jesu Raja$^{3}$
$^{1,3}$Department of Mathematics
Loyola College
Chennai, 600 034, INDIA
$^{2}$Department of Mathematics
Stella Maris College
Chennai, 600 086, INDIA

Abstract. A molecular graph is a simple graph such that its vertices correspond to the atoms and the edges to the bonds. An edge set $M$ of a graph $G$ is called a matching if no two edges in $M$ have a common end vertex. A matching $M$ of $G$ is perfect if every vertex of $G$ is incident with an edge in $M$. In organic molecular graphs, perfect matchings correspond to Kekule structures playing an important role in analysis of the resonance energy and stability of hydrocarbon compounds. The anti-Kekule number is the smallest number of edges that must be removed from a connected graph with a perfect matching so that the graph remains connected, but has no perfect matchings. In this paper we find the anti-kekule number for silicate, oxide and honeycomb networks.

Received: May 9, 2013

AMS Subject Classification: 05C70

Key Words and Phrases: anti-Kekule number, silicate, oxide and honeycomb networks

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DOI: 10.12732/ijpam.v86i6.15 How to cite this paper?
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 86
Issue: 6