Neighborhood condition for all fractional (g, f, n′, m)-critical deleted graphs
نویسندگان
چکیده
منابع مشابه
a neighborhood :union: condition for fractional $(k,n',m)$-critical deleted graphs
a graph $g$ is called a fractional $(k,n',m)$-critical deleted graph if any $n'$ vertices are removed from $g$ the resulting graph is a fractional $(k,m)$-deleted graph. in this paper, we prove that for integers $kge 2$, $n',mge0$, $nge8k+n'+4m-7$, and $delta(g)ge k+n'+m$, if $$|n_{g}(x)cup n_{g}(y)|gefrac{n+n'}{2}$$ for each pair of non-adjac...
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A graph G is called a fractional (k, n′,m)-critical deleted graph if any n′ vertices are removed from G the resulting graph is a fractional (k,m)-deleted graph. In this paper, we prove that for integers k ≥ 2, n′,m ≥ 0, n ≥ 8k + n′ + 4m− 7, and δ(G) ≥ k + n′ +m, if |NG(x) ∪NG(y)| ≥ n+ n′ 2 for each pair of non-adjacent vertices x, y of G, then G is a fractional (k, n′,m)-critical deleted graph....
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All graphs considered in this paper are finite, loopless, and without multiple edges. The notation and terminology used but undefined in this paper can be found in [2]. Let G be a graph with the vertex set V (G) and the edge set E(G). For a vertex x ∈ V (G), we use dG(x) and NG(x) to denote the degree and the neighborhood of x in G, respectively. Let δ(G) denote the minimum degree of G. For any...
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A graph G is called a fractional (g, f)-deleted graph if G - {e} admits a fractional (g, f)-factor for any e ∈ E(G). A graph G is called a fractional (g, f, n)-critical deleted graph if, after deleting any n vertices from G, the resulting graph is still a fractional (g, f)-deleted graph. The toughness, as the parameter for measuring the vulnerability of communication networks, has received sign...
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Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k + 3− 4 √ 2(k − 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G ...
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ژورنال
عنوان ژورنال: Open Physics
سال: 2018
ISSN: 2391-5471
DOI: 10.1515/phys-2018-0071