On the order and size of s-geodetic digraphs with given connectivity
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On the order and size of s-geodetic digraphs with given connectivity
A digraph G = (V, E) with diameter D is said to be s-geodetic, for 1 ≤ s ≤ D, if between any pair of (not necessarily different) vertices x, y ∈ V there is at most one x → y path of length ≤ s. Thus, any loopless digraph is at least 1-geodetic. A similar definition applies for a graph G, but in this case the concept is closely related to its girth g, for then G is s-geodetic with s = b(g − 1)/2...
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Bounds on the size of graphs of given order and up/down-connectivity
The /-connectivity ~c/(G) of a graph G of order p ~ > / I is the minimum number of vertices that are required to be deleted from G to produce a graph with at least f components or with fewer than /' vertices. Extremal graphs are investigated and bounds established on the number of edges in graphs of given order and f-connectivity. @ 1999 Elsevier Science B.V, All rights reserved
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00314-7