Neighborhood unions and cyclability of graphs
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چکیده
منابع مشابه
Neighborhood unions and cyclability of graphs
A graph G is said to be cyclable if for each orientation → G of G, there exists a set S of vertices such that reversing all the arcs of → G with one end in S results in a hamiltonian digraph. Let G be a 3-connected graph of order n¿ 36. In this paper, we show that if for any three independent vertices x1, x2 and x3, |N (x1) ∪ N (x2)|+ |N (x2) ∪ N (x3)|+ |N (x3) ∪ N (x1)|¿ 2n+ 1, then G is cycla...
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We investigate the relationship between the cardinality of the union of the neighborhoods of an arbitrary pair of nonadjacent vertices and various hamiltonian type properties in graphs. In particular, we show that if G is 2-connected, of order p 2 3 and if for every pair of nonadjacent vertices x and y: (a) IN(x) u N( y)l 2 (p 1)/2, then G is traceable, (b) IN(x) u N( y)l 2 (2p 1)/3, then G is ...
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Bauer, D., G. Fan and H.J. Veldman, Hamiltonian properties of graphs with large neighborhood unions, Discrete Mathematics 96 (1991) 33-49. Let G be a graph of order n, a k =min{~ki=ld(vi): {V 1 . . . . . Vn} is an independent set of vertices in G}, NC=min{IN(u) 13N(v) l :uv~E(G)} and NC2=min{IN(u) t3 N(v)l: d(u, v)=2}. O.~ proved that G is hamiltonian if o2~>n ~>3, while Faudree et al. proved t...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2004
ISSN: 0166-218X
DOI: 10.1016/j.dam.2003.05.002