It has been proved that if the diameter D of a digraph G satisfies D Յ 2ᐉ Ϫ 2, where ᐉ is a parameter which can be thought of as a generalization of the girth of a graph, then G is superconnected. Analogously, if D Յ 2ᐉ Ϫ 1, then G is edge-superconnected. In this paper, we studied some similar condi
Connectedness of digraphs and graphs under constraints on the conditional diameter
✍ Scribed by X. Marcote; C. Balbuena; J. Fàbrega
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 206 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Recently, it was proved that if the diameter D of a graph G is small enough in comparison with its girth, then G is maximally connected and that a similar result also holds for digraphs. More precisely, if the diameter D of a digraph G satisfies D 5 21 -1, then G has maximum connectivity ( K = 6 ) .
denote the set of all m × n {0, 1}-matrices with row sum vector R and column sum vector S. Suppose A(R, S) ] ". The interchange graph G(R, S) of A(R, S) was defined by Brualdi in 1980. It is the graph with all matrices in A(R, S) as its vertices and two matrices are adjacent provided they differ by
We prove that if s and t are positive integers and if G is a triangle-free graph with minimum degree s + t, then the vertex set of G has a decomposition into two sets which induce subgraphs of minimum degree at least s and t, respectively.
We show that, in a claw-free graph, Hamilton-connectedness is preserved under the operation of local completion performed at a vertex with 2-connected neighborhood. This result proves a conjecture by Bollobás et al.