IJPAM: Volume 87, No. 6 (2013)

TOTAL GRAPH OF $K_n$ AND $K_{m,n}$

M.M. Akbar Ali
Department of Mathematics
Karunya University
Coimbatore, 641 114, Tamil Nadu, INDIA

Abstract. Tulgeity $\tau (G)$ of a graph $G$ is the maximum number of vertex disjoint cycles contained in $G$. In this paper the basic results on tulgeity of a graph have been reviewed and the formula for the tulgeity of the middle and total graph of complete graph and complete bigraph are derived. Also an upper bound for the tulgeity of middle graph of any graph is presented and the graph for which the tulgeity attains its upper bound has been classified.

Received: September 6, 2013

AMS Subject Classification: 05C70, 05C75, 05C76

Key Words and Phrases: tulgeity, line graph, total graph, complete graph and complete bigraph

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DOI: 10.12732/ijpam.v87i6.7 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: 87
Issue: 6