Abstract:

The graph marked F_n,4 that is formed by n pieces of 4cycles with one common vertice in order. Let u_i1 and u_i2 be two vertices in graph F_n,4, which connect u_i1 and u_i2 with m paths of length 2 for u_i1v_iju_i2(i,j=1,2,…,n). The resulting graphs are denoted as m-F_n,4. Let G represent the graph obtained by connecting every vertex of graph m-F_n,4 isolated vertex w to an edge of it. Let m-F_n,4+E_n(m+1) be the graph obtained from G by attaching n(m+1) pendent edges to the vertex w of graph G. The constructor method gives graceful labeling of m-F_n,4 and m-F_n,4+E_n(m+1), thus proving graceful graphs m-F_n,4 and m-F_n,4+E_n(m+1). Thus, a series of graceful graphs can be constructed from one graceful graph.

Key words: 4-cycles, graceful graph, graceful labeling