ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES - G. Rajasekaran; L. Uma (Ural Mathematical Journal)
In this paper, we prove the following results: 1) the disjoint union of \(n≥ 2\) isomorphic copies of the graph which is obtained by adding a pendent edge to each vertices of the cycle of order 4 admits \(α\)-valuation; 2) the disjoint union of two isomorphic copies of the graph which is obtained by adding \(n≥ 1\) pendent edge to each vertices of the cycle of order 4 is admits \(α\)-valuation; 3) the disjoint union of two isomorphic copies of the graph obtained by adding a pendent edge to each vertex of the cycle of order \(4m\) admits \(α\)-valuation; 4) the disjoint union of two non-isomorphic copies of the graph obtained by adding a pendent edge to each vertices of the cycle of order \(4m\) and \(4m-2\) admits \(α\)-valuation; 5) the disjoint union of two isomorphic copies of the graph which is obtained by adding a pendant edge to each vertex of the cycle of order \(4m-1(4m+2)\) is admitted graceful (\(α\)-valuation).