ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES

Abstract

In this paper, we prove the following results: 1) the disjoint union of \(n\geq 2\) isomorphic copies of the graph which is obtained by adding a pendent edge to each vertices of the cycle of order 4 admits \(\alpha\)-valuation; 2) the disjoint union of two isomorphic copies of the graph which is obtained by adding \(n\geq 1\) pendent edge to each vertices of the cycle of order 4 is admits \(\alpha\)-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 \(\alpha\)-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 \(\alpha\)-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 (\(\alpha\)-valuation).

Keywords

• hairy cycles, graceful valuation, alpha valuation