Cycle multiplicity of a graph G is the maximum number of edge disjoint cycles in G. In this paper, we find the cycle multiplicity of total graph of cycles C n , paths P n , and star graph K 1 , n respectively.
Tulgeity τ (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.
The notion of equitable coloring was introduced by Meyer in 1973. In this paper we obtain interesting results regarding the equitable chromatic number for the total graph of complete bigraphs , the central graph of cycles and the central graph of paths .
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