Sufficient conditions for locally connected graphs
نویسندگان
چکیده
منابع مشابه
Sufficient conditions for maximally edge-connected and super-edge-connected
Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...
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A connected graph with edge connectivity λ and minimum degree δ is called maximally edge-connected if λ = δ. A strongly connected digraph with arc connectivity λ and minimum degree δ is called maximally arc-connected if λ = δ. In this paper, some new sufficient conditions are presented for maximally edge-connected graphs and arc-connected digraphs. We only consider finite graphs (digraphs) with...
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A graph G is s-Hamiltonian if for any S ⊆ V (G) of order at most s, G−S has a Hamiltonian-cycle, and s-Hamiltonian connected if for any S ⊆ V (G) of order at most s, G − S is Hamiltonian-connected. Let k > 0, s ≥ 0 be two integers. The following are proved in this paper: (1) Let k ≥ s+ 2 and s ≤ n− 3. If G is a k-connected graph of order n and if max{d(v) : v ∈ I} ≥ (n+s)/2 for every independen...
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We propose a conjecture regarding the lower bound for the number of edges in locally k-connected graphs and we prove it for k = 2. In particular, we show that every connected locally 2-connected graph is M3-rigid. For the special case of surface triangulations, this fact was known before using topological methods. We generalize this result to all locally 2-connected graphs and give a purely com...
متن کاملSufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs
Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree and its in-degree . Now let D be a digraph with minimum degree and edge-connectivity If is real number, then the zeroth-order general Randic index is defined by . A digraph is maximally edge-connected if . In this paper we present sufficient condi...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1974
ISSN: 0528-2195
DOI: 10.21136/cpm.1974.117861