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
In this paper, we investigate the reliability analysis of a powerloom plant by using interval valued intuitionistic fuzzy sets (IVIFS). Herein, we modeled a powerloom plant as a gracefully degradable system having two...In this paper, we investigate the reliability analysis of a powerloom plant by using interval valued intuitionistic fuzzy sets (IVIFS). Herein, we modeled a powerloom plant as a gracefully degradable system having two units A(n) and B(m) connected in series. The reliability ofncomponents of unitAandmcomponents of unitBis assumed to be an IVIFS defined over the universe of discourse [0, 1]. Thus, the reliability of the system obtained is an IVIFS that covers the inherited uncertainty in data collection and reliability evaluation of a powerloom plant.展开更多
Graceful form is one of the aesthetic forms.The graceful form gives a pleasant mood,purity,elegance, gentleness and represents an aesthetic form of vitality.The beautiful form in the Mongolian epic not only reflects t...Graceful form is one of the aesthetic forms.The graceful form gives a pleasant mood,purity,elegance, gentleness and represents an aesthetic form of vitality.The beautiful form in the Mongolian epic not only reflects the Mongolian aesthetics and clarifies the artistic form of the epic.This article seeks to interpret and explain the morphological features of the graceful form in Mongolian epics and its aesthetic value.展开更多
The present paper shows the coordinates of a tree and its vertic es, defines a kind of Trees with Odd-Number Radiant Type (TONRT), deals with th e gracefulness of TONRT by using the edge-moving theorem, and uses gra...The present paper shows the coordinates of a tree and its vertic es, defines a kind of Trees with Odd-Number Radiant Type (TONRT), deals with th e gracefulness of TONRT by using the edge-moving theorem, and uses graceful TON RT to construct another class of graceful trees.展开更多
LOCATED in GuizhouProvince, southwesternChina, Qianxinan Bouyei-Miao AutonomousPrefecture is a tourist destination,due to its extraordinary naturalenvironment and distinctive
Let G(V,E) be a simple graph and G^k be a k-power graph defined byV(G~*) = V(G), E(G^k) = E(G) ∪{uv|d(u,v) =k} for natural number k. In this paper,it is proved that P_n^3 is a graceful graph.
Functionally Graded Concrete （FGC） is fabricated at the Institute for Lightweight Structures and Conceptual Design （ILEK） by using a layer-by-layer technique with two different technological procedures： casting a...Functionally Graded Concrete （FGC） is fabricated at the Institute for Lightweight Structures and Conceptual Design （ILEK） by using a layer-by-layer technique with two different technological procedures： casting and dry spraying. Functional gradations are developed from two reference mixtures with diametrically opposed characteristics in terms of density, porosity, compression strength and elasticity modulus. In this study the first mixture consists of Normal Density Concrete （NDC）, with density about 2160 kg·m^-3 while the second mixture helps to obtain a very lightweight concrete, with density about 830 kg·m^-3. The FGC specimens have layers with different alternating porosities and provide superior deformability capacity under bulk compression compared to NDC specimens. In addition, the FGC specimens experienced a graceful failure behaviour, absorbing high amounts of energy during extended compression paths. The porosity variation inside the layout of tested specimens is inspired by the internal structure of sea urchin spines of heterocentrotus mammillatus, a promising role model for energy absorption in biomimetic engineering.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
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.
文摘In this paper, we investigate the reliability analysis of a powerloom plant by using interval valued intuitionistic fuzzy sets (IVIFS). Herein, we modeled a powerloom plant as a gracefully degradable system having two units A(n) and B(m) connected in series. The reliability ofncomponents of unitAandmcomponents of unitBis assumed to be an IVIFS defined over the universe of discourse [0, 1]. Thus, the reliability of the system obtained is an IVIFS that covers the inherited uncertainty in data collection and reliability evaluation of a powerloom plant.
文摘Graceful form is one of the aesthetic forms.The graceful form gives a pleasant mood,purity,elegance, gentleness and represents an aesthetic form of vitality.The beautiful form in the Mongolian epic not only reflects the Mongolian aesthetics and clarifies the artistic form of the epic.This article seeks to interpret and explain the morphological features of the graceful form in Mongolian epics and its aesthetic value.
文摘The present paper shows the coordinates of a tree and its vertic es, defines a kind of Trees with Odd-Number Radiant Type (TONRT), deals with th e gracefulness of TONRT by using the edge-moving theorem, and uses graceful TON RT to construct another class of graceful trees.
文摘LOCATED in GuizhouProvince, southwesternChina, Qianxinan Bouyei-Miao AutonomousPrefecture is a tourist destination,due to its extraordinary naturalenvironment and distinctive
文摘Let G(V,E) be a simple graph and G^k be a k-power graph defined byV(G~*) = V(G), E(G^k) = E(G) ∪{uv|d(u,v) =k} for natural number k. In this paper,it is proved that P_n^3 is a graceful graph.
文摘Functionally Graded Concrete （FGC） is fabricated at the Institute for Lightweight Structures and Conceptual Design （ILEK） by using a layer-by-layer technique with two different technological procedures： casting and dry spraying. Functional gradations are developed from two reference mixtures with diametrically opposed characteristics in terms of density, porosity, compression strength and elasticity modulus. In this study the first mixture consists of Normal Density Concrete （NDC）, with density about 2160 kg·m^-3 while the second mixture helps to obtain a very lightweight concrete, with density about 830 kg·m^-3. The FGC specimens have layers with different alternating porosities and provide superior deformability capacity under bulk compression compared to NDC specimens. In addition, the FGC specimens experienced a graceful failure behaviour, absorbing high amounts of energy during extended compression paths. The porosity variation inside the layout of tested specimens is inspired by the internal structure of sea urchin spines of heterocentrotus mammillatus, a promising role model for energy absorption in biomimetic engineering.
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.
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
