Abstract
Tulgeity �(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. Cycle is a significant feature of a graph. The analysis of cycle plays an important role in the design and development of some graph model. Several problems of finding shortest path, shortest spanning trees, least cost Hamiltonian cycles, etc., of a graph have been studied. We discuss the problems of finding the maximum number of vertex disjoint cycles. We consider finite, simple, undirected graph G(V (G),E(G)) where V (G) and E(G) represent vertex set and edge set of G respectively. p and q denote the
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