๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the relationship between the diameter and the size of a boundary of a directed graph

โœ Scribed by Shuji Jimbo; Akira Marouka


Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
480 KB
Volume
50
Category
Article
ISSN
0020-0190

No coin nor oath required. For personal study only.


๐Ÿ“œ SIMILAR VOLUMES


On the Spectrum, the Growth, and the Dia
โœ N. Hajaj ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 171 KB

A lower bound is given for the harmonic mean of the growth in a finite undirected graph 1 in terms of the eigenvalues of the Laplacian of 1. For a connected graph, this bound is tight if and only if the graph is distance-regular. Bounds on the diameter of a ``sphere-regular'' graph follow. Finally,

The generalized diameter of a graph
โœ Chih-Kang Eric Chen; R. S. Garfinkel ๐Ÿ“‚ Article ๐Ÿ“… 1982 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 198 KB

## Abstract We generalize the concept of the diameter of a graph __G__ = (__N, A__) to allow for location of points not on the nodes. It is shown that there exists a finite set of candidate points which determine this __generalized diameter.__ Given the matrix of shortest paths, an __o__ (|__A__|^2

A generalisation of the diameter of a gr
โœ Douglas D. Grant ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 262 KB

## We prove the following theorem. If G b a connected finite graph of order p, and S is a k-subset of V(G) (where k 2 2), then there is a pair of vertices in S which are at a dbtance ~2 [(p -1)/k] if k does not divide p, and ~2 I@ -1)/k j + 1 otherwise.

On the cycle polytope of a directed grap
โœ Egon Balas; Maarten Oosten ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 185 KB ๐Ÿ‘ 2 views
On the spectral radius of a directed gra
โœ Kwapisz, Jaroslaw ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 314 KB ๐Ÿ‘ 2 views

We provide upper estimates on the spectral radius of a directed graph. In particular w e prove that the spectral radius is bounded by the maximum of the geometric mean of in-degree and out-degree taken over all vertices.

On the distance matrix of a directed gra
โœ R. L. Graham; A. J. Hoffman; H. Hosoya ๐Ÿ“‚ Article ๐Ÿ“… 1977 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 144 KB ๐Ÿ‘ 2 views

## Abstract In this note, we show how the determinant of the distance matrix __D(G__) of a weighted, directed graph __G__ can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks __G~i~__ of __G__. In particular, when cof __D(G__), the sum of the cofactors of _