Research on the gracefulness of graphs(P_2∨C_n) ∪St( m)and(P_2∨P_n) ∪St(m)
Yu Yan · Journal of Henan Polytechnic University · 2013
This article mainly investigate the the gracefulness of unconnected graphs(P2∨Cn) USt(m) and(P2∨Pn) USt(m),showing that for n≡0(mod4),n≥8,m≥n-1,(P2∨Cn) USt(m) is a graceful graph;for n≡0(mod4),n≥8,m1=(n/2)- 1,m2≥(n/2),(P2∨Cn) USt(m1) ∪St(m2) is a graceful graph;for n≡0(mod2),n≥6,m≥(n/2),(P2∨Pn) ∪St(m) is a graceful graph; and for the situation that n≡0(mod2),n≥6,m1=(n/2)- 1,m1+ m2≥(n/2),(P2∨Pn) ∪St(m1) ∪St(m2) is a graceful graph.