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The diameter of a disc filling a loop in the universal covering of a Riemannian manifold M may be measured extrinsically using the distance function on the ambient space or intrinsically using the ind...
We give a tight upper bound on the polygonal diameter of the interior, resp. exterior, of a simple n-gon, n ≥ 3, in the plane as a function of n, and describe an n-gon (n ≥ 3) for which both upper bou...
In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k2 k ≤ C. This extends a conj...
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. ...
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees (“Otter trees”), when trees of a given size are taken with equal likelihood. The height of...
We prove a bound for the geodesic diameter of a subset of the unit ball in Rn described by a fixed number of quadratic equations and inequalities,which is polynomial in n, whereas the known bound for ...
Classification of Regular Planar Graphs with Diameter two     graph    regular    diameter    planar    outer planar       2007/12/11
In the present paper, the regular planar graphs with diameter two are classified.

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