Let G be a graph, an independent set Y in G is called an essential independent set (or essential set for simplicity), if there is {y 1,y 2} Y such that dist (y 1,y 2)=2. In this paper, we wi...Let G be a graph, an independent set Y in G is called an essential independent set (or essential set for simplicity), if there is {y 1,y 2} Y such that dist (y 1,y 2)=2. In this paper, we will use the technique of the vertex insertion on l connected ( l=k or k+1,k≥2 ) claw free graphs to provide a unified proof for G to be hamiltonian or 1 hamiltonian, the sufficient conditions are expressed by the inequality concerning ∑ki=0N(Y i) and n(Y) for each essential set Y={y 0,y 1,...,y k} of G , where Y i={y i,y i-1 ,...,y i-(b-1) }Y for i∈{0,1,...,k} (the subscriptions of y j ’s will be taken modulo k+1 ), b ( 0【b【k+1 ) is an integer, and n(Y)={v∈V(G): dist (v,Y)≤2 }.展开更多
Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric(p. q. metric) p: L^x xL^x -[0,∞] where L is acompletely distributive latt...Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric(p. q. metric) p: L^x xL^x -[0,∞] where L is acompletely distributive lattice, and the associated family of neighborhood mappings {Dr |r>O}. Thefuzzy metric space in Erceg's sense is denoted by (L^x, p, Dr) since there exists a one to one correspondence between fuzzy p. q. metrics and associatcd families of neighborhood mapping, a family{Dr|r>0}satisfying certain conditions is also callcd a (standard) fuzzy p. q metric. In [2] Liang defimed apointwise fuzzy p. q. metric d: P(L^x)×P(L^x)-[0, ∞) and applicd it to the construction of theproduct fuzzy metric. In this paper, we give axiomatic definitions of molcculewise and展开更多
In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and t...In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.展开更多
文摘Let G be a graph, an independent set Y in G is called an essential independent set (or essential set for simplicity), if there is {y 1,y 2} Y such that dist (y 1,y 2)=2. In this paper, we will use the technique of the vertex insertion on l connected ( l=k or k+1,k≥2 ) claw free graphs to provide a unified proof for G to be hamiltonian or 1 hamiltonian, the sufficient conditions are expressed by the inequality concerning ∑ki=0N(Y i) and n(Y) for each essential set Y={y 0,y 1,...,y k} of G , where Y i={y i,y i-1 ,...,y i-(b-1) }Y for i∈{0,1,...,k} (the subscriptions of y j ’s will be taken modulo k+1 ), b ( 0【b【k+1 ) is an integer, and n(Y)={v∈V(G): dist (v,Y)≤2 }.
文摘Erceg in [1] extended the Hausdorff distance function betwen subsets of a set X to fuzzy settheory, and introduced a fuzzy pseudo-quasi-metric(p. q. metric) p: L^x xL^x -[0,∞] where L is acompletely distributive lattice, and the associated family of neighborhood mappings {Dr |r>O}. Thefuzzy metric space in Erceg's sense is denoted by (L^x, p, Dr) since there exists a one to one correspondence between fuzzy p. q. metrics and associatcd families of neighborhood mapping, a family{Dr|r>0}satisfying certain conditions is also callcd a (standard) fuzzy p. q metric. In [2] Liang defimed apointwise fuzzy p. q. metric d: P(L^x)×P(L^x)-[0, ∞) and applicd it to the construction of theproduct fuzzy metric. In this paper, we give axiomatic definitions of molcculewise and
基金the National Natural Science Foundation of China (60274016)the Project of Scientific Research in Hight Education Bureau Liaoning Province (2023901018).
文摘In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.
