
Summary: In this paper, it has been shown that the hairy cycle \(C_{n}\odot rK_{1},\) \(n\equiv 3\pmod 4\), the graph obtained by adding pendant edge to each pendant vertex of hairy cycle \(C_{n}\odot 1K_{1}\), \(n\equiv 0\pmod 4\), double graph of path \(P_{n}\) and double graph of comb \(P_{n}\odot 1K_{1}\) are \(k\)-graceful.
Graph labelling (graceful graphs, bandwidth, etc.), \(k\)-graceful labeling, hairy cycle, double graph, \(k\)-graceful graphs
Graph labelling (graceful graphs, bandwidth, etc.), \(k\)-graceful labeling, hairy cycle, double graph, \(k\)-graceful graphs
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