On the gracefulness of ∪from i=1 to n ∧from j=1 to m_i A(n_j)
Wang Chun-yue · Journal of Liaoning Normal University · 2011
The Bipartite graph A(n)=(X,Y,E) is a graph as one obtained by joining u1 and u2 to a new vertex vi for i=0,1,…,n-1,let X={u1,u2},Y={v0,v1,…vn-1},A(nj)=(Xj,Yj,Ej).∧from j=1 to m A(nj) is a graph as one obtained by joining vjnj-1 to uj+12 with an edge for j=1,2,…,m-1.∪from i=1 to n ∧from j=1 to m_i A(n_j) is the disjoint union of ∧from j=1 to m_i for i=1,2,…,n.In this paper,we prove that ∪from i=1 to n ∧from j=1 to m_i A(n_j) is graceful and alternating graph.