منابع مشابه
Dominating cycles in halin graphs
A cycle in a graph is dominating if every vertex lies at distance at most one from the cycle and a cycle is D-cycle if every edge is incident with a vertex of the cycle. In this paper, first we provide recursive formulae for finding a shortest dominating cycle in a Hahn graph; minor modifications can give formulae for finding a shortest D-cycle. Then, dominating cycles and D-cycles in a Halin g...
متن کاملThe k-dominating cycles in graphs
For a graph G, let σ̄k+3(G) = min {d(x1) + d(x2) + · · · + d(xk+3) − |N(x1) ∩ N(x2) ∩ · · · ∩ N(xk+3)| | x1, x2, · · · , xk+3 are k + 3 independent vertices in G}. In [5], H. Li proved that if G is a 3-connected graph of order n and σ̄4(G) ≥ n+3, then G has a maximum cycle such that each component of G−C has at most one vertex. In this paper, we extend this result as follows. Let G be a (k + 2)-c...
متن کاملA note on Hamiltonian cycles in generalized Halin graphs
We show that every 2-connected (2)-Halin graph is Hamiltonian.
متن کاملDominating cycles in triangle-free graphs
A cycle C in a graph G is said to be dominating if E(G−C) = ∅. Enomoto et al. showed that if G is a 2-connected triangle-free graph with α(G) ≤ 2κ(G) − 2, then every longest cycle is dominating. But it is unknown whether the condition on the independence number is sharp. In this paper, we show that if G is a 2-connected triangle-free graph with α(G) ≤ 2κ(G) − 1, then G has a longest cycle which...
متن کاملLong dominating cycles in graphs 1
Let G be a connected graph of order n, and let NC2(G) denote min{[N(u)UN(v)[: dist(u, v )= 2}, where dist(u, v) is the distance between u and v in G. A cycle C in G is called a dominating cycle, if V(G)\V(C) is an independent set in G. In this paper, we prove that if G contains a dominating cycle and ~ ~> 2, then G contains a dominating cycle of length at least min{n,2NC2(G)3}. ~ 1997 Elsevier ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90362-l