Induced weak cycle number of path and its derived graphs
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Let G = (V, E) be a simple connected graph. The induced weak cycle partition of G is defined as the partition of V(G) into subsets such that each subset induces a cycle or K2 or K1. The induced weak cycle number of G, denoted by ρ_wc (G), is the minimum cardinality taken over all induced weak cycle partitions. In this paper, the concept of induced weak cycle number is introduced and induced weak cycle number of path and some of its derived graphs are studied.
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