The present paper deals with the gracefulness of unconnected graph （jC_（4n））∪P_m,and proves the following result：for positive integers n,j and m with n≥1,j≥2,the unconnected graph（jC_（4n））∪P_m is a gracef...The present paper deals with the gracefulness of unconnected graph （jC_（4n））∪P_m,and proves the following result：for positive integers n,j and m with n≥1,j≥2,the unconnected graph（jC_（4n））∪P_m is a graceful graph for m=j-1 or m≥n＋j,where C_（4n） is a cycle with 4n vertexes,P_m is a path with m＋1 vertexes,and（jC_（4n））∪P_m denotes the disjoint union of j-C_（4n） and P_m.展开更多
Two kinds of unconnected double fan graphs with even vertices,(P^((1))_(1)∨(P^((1))_(2n)∪P^((2))_(2n)))∪P_(2n+1)∪(P_(1)^((2))∨K_(2n))and(P_(1)^((1))∨(P^((1))_(2n)∪P^((2))_(2n)))∪(P_(1)^((2))∨K_((1))^(2n))∪(P...Two kinds of unconnected double fan graphs with even vertices,(P^((1))_(1)∨(P^((1))_(2n)∪P^((2))_(2n)))∪P_(2n+1)∪(P_(1)^((2))∨K_(2n))and(P_(1)^((1))∨(P^((1))_(2n)∪P^((2))_(2n)))∪(P_(1)^((2))∨K_((1))^(2n))∪(P^((3))_(1)∨K_((2))^(2n))were presented.For natural number n∈N,n≥1,the two graphs are all graceful graphs,where P^((1))_(2n),P^((2))_(2n)are even-vertices path,P_(2n+1)is odd-vertices path,K_(2n),K^((1))_(2n),K^((2))_(2n)are the complement of graph K_(2 n),G_(1)∨G_(2)is the join graph of G_(1)and G_(2).展开更多
In the paper, we study the gracefulness of several unconnected graphs related to wheel. For natural number p ≥ 1, t ≥ 1 , let n = 2t ＋ 3,2t ＋ 4 , which proved W. U K （1） p,t U K（2） is graceful; for p≥1, t≥1 ...In the paper, we study the gracefulness of several unconnected graphs related to wheel. For natural number p ≥ 1, t ≥ 1 , let n = 2t ＋ 3,2t ＋ 4 , which proved W. U K （1） p,t U K（2） is graceful; for p≥1, t≥1 ,let n=2t＋3,2t＋4, then Wn,2n＋1 U K（1）p,t U K（2） p,t is graceful and for m ≥ 1, r ≥ 1 , let n = 2m ＋ 5, Wn,2n＋1 U （C3 v Km） U St（r） is graceful.展开更多
The GRACE(Gravity Recovery and Climate Experiment)space mission recorded temporal variation characteristics of the global gravity field at decadal timescales.The gravity data have been shown to capture the dynamics of...The GRACE(Gravity Recovery and Climate Experiment)space mission recorded temporal variation characteristics of the global gravity field at decadal timescales.The gravity data have been shown to capture the dynamics of flows within the outer core and their effects on the core-mantle boundary.We first aim to remove global surface process gravity signals from the GRACE data.We then construct the global core magnetic field according to the CHAOS-7 model.Finally,we apply the blind source separation method to decompose the processed gravity signals and core magnetic signals and compute the power spectral density of the gravity and magnetic field signals by using the Lomb-Scargle periodogram approach.We have discovered a signal cycle(of~6 years)in the principal components of the core magnetic and gravity signals,potentially as a result of deep Earth processes.The main principal components of the core magnetic and gravity signals reveal that the variation trends in the second-order time derivative of the core magnetic field are similar to those in the gravity field.After 2014,the second-order time derivative of the core magnetic field exhibited linear and rapid change characteristics,which were the same as the change in the gravity field and are consistent with existing research results.展开更多
A digraph D（V, E） is said to be graceful if there exists an injection f ： V（G） →{0, 1,... , ｜E｜} such that the induced function f＇ ： E（G） --~ {1, 2,… , ｜E｜} which is defined by f＇ （u, v） = [f（v） - ...A digraph D（V, E） is said to be graceful if there exists an injection f ： V（G） →{0, 1,... , ｜E｜} such that the induced function f＇ ： E（G） --~ {1, 2,… , ｜E｜} which is defined by f＇ （u, v） = [f（v） - f（u）] （rood ｜E｜＋ 1） for every directed edge （u, v） is a bijection. Here, f is called a graceful labeling （graceful numbering） of D（V, E）, while f＇ is called the induced edge＇s graceful labeling of D. In this paper we discuss the gracefulness of the digraph n- Cm and prove that n. Cm is a graceful digraph for m = 15, 17 and even展开更多
文摘The present paper deals with the gracefulness of unconnected graph （jC_（4n））∪P_m,and proves the following result：for positive integers n,j and m with n≥1,j≥2,the unconnected graph（jC_（4n））∪P_m is a graceful graph for m=j-1 or m≥n＋j,where C_（4n） is a cycle with 4n vertexes,P_m is a path with m＋1 vertexes,and（jC_（4n））∪P_m denotes the disjoint union of j-C_（4n） and P_m.
基金the National Natural Science Foundation of China(11702094)the Fundamental Research Funds for the Central University(3142015045)。
文摘Two kinds of unconnected double fan graphs with even vertices,(P^((1))_(1)∨(P^((1))_(2n)∪P^((2))_(2n)))∪P_(2n+1)∪(P_(1)^((2))∨K_(2n))and(P_(1)^((1))∨(P^((1))_(2n)∪P^((2))_(2n)))∪(P_(1)^((2))∨K_((1))^(2n))∪(P^((3))_(1)∨K_((2))^(2n))were presented.For natural number n∈N,n≥1,the two graphs are all graceful graphs,where P^((1))_(2n),P^((2))_(2n)are even-vertices path,P_(2n+1)is odd-vertices path,K_(2n),K^((1))_(2n),K^((2))_(2n)are the complement of graph K_(2 n),G_(1)∨G_(2)is the join graph of G_(1)and G_(2).
基金Supported by the Natural Science Foundation of Beijing(1102015)University Scientific Research Project of Hebei Province(Z2014032)the Fundamental Research Funds for the Central Universities(HKXJZD201402,2011B019,3142013025,3142014127)
文摘In the paper, we study the gracefulness of several unconnected graphs related to wheel. For natural number p ≥ 1, t ≥ 1 , let n = 2t ＋ 3,2t ＋ 4 , which proved W. U K （1） p,t U K（2） is graceful; for p≥1, t≥1 ,let n=2t＋3,2t＋4, then Wn,2n＋1 U K（1）p,t U K（2） p,t is graceful and for m ≥ 1, r ≥ 1 , let n = 2m ＋ 5, Wn,2n＋1 U （C3 v Km） U St（r） is graceful.
基金the National Natural Science Foundation of China(Grant Nos.42274003,41974007,and 41774019).
文摘The GRACE(Gravity Recovery and Climate Experiment)space mission recorded temporal variation characteristics of the global gravity field at decadal timescales.The gravity data have been shown to capture the dynamics of flows within the outer core and their effects on the core-mantle boundary.We first aim to remove global surface process gravity signals from the GRACE data.We then construct the global core magnetic field according to the CHAOS-7 model.Finally,we apply the blind source separation method to decompose the processed gravity signals and core magnetic signals and compute the power spectral density of the gravity and magnetic field signals by using the Lomb-Scargle periodogram approach.We have discovered a signal cycle(of~6 years)in the principal components of the core magnetic and gravity signals,potentially as a result of deep Earth processes.The main principal components of the core magnetic and gravity signals reveal that the variation trends in the second-order time derivative of the core magnetic field are similar to those in the gravity field.After 2014,the second-order time derivative of the core magnetic field exhibited linear and rapid change characteristics,which were the same as the change in the gravity field and are consistent with existing research results.
文摘A digraph D（V, E） is said to be graceful if there exists an injection f ： V（G） →{0, 1,... , ｜E｜} such that the induced function f＇ ： E（G） --~ {1, 2,… , ｜E｜} which is defined by f＇ （u, v） = [f（v） - f（u）] （rood ｜E｜＋ 1） for every directed edge （u, v） is a bijection. Here, f is called a graceful labeling （graceful numbering） of D（V, E）, while f＇ is called the induced edge＇s graceful labeling of D. In this paper we discuss the gracefulness of the digraph n- Cm and prove that n. Cm is a graceful digraph for m = 15, 17 and even
