𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Large bipartite graphs with given degree and diameter

✍ Scribed by C. Delorme

Publisher
John Wiley and Sons
Year
1985
Tongue
English
Weight
393 KB
Volume
9
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

W e give constructions of bipartite graphs with maximum A, diameter D on B vertices. such :bat for every D 3 2 :he !im i nf , . . , B . A'"' = b,, > 0. W e also improve similar results on ordinary graphs, for example, w e prove that lim, , , N -A-." = 1 if D is 3 or 5. This is a partial answer to a problem of Bollobas.

πŸ“œ SIMILAR VOLUMES

Some large graphs with given degree and
Some large graphs with given degree and diameter
✍ I. Alegre; M. A. Fiol; J. L. A. Yebra πŸ“‚ Article πŸ“… 1986 πŸ› John Wiley and Sons 🌐 English βš– 196 KB πŸ‘ 1 views

This paper considers the (A, 0 ) problem: to maximize the order of graphs with given maximum degree A and diameter 0, of importance for its implications in the design of interconnection networks. Two cubic graphs of diameters 5 and 8 and orders 70 and 286, respectively, and a graph of degree 5, diam

New large graphs with given degree and d
New large graphs with given degree and diameter six
✍ GοΏ½mez, J.; Pelayo, I.; Balbuena, C. πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 166 KB πŸ‘ 2 views

In this paper, a method for obtaining large diameter 6 graphs by replacing some vertices of a Moore bipartite diameter 6 graph with complete K h graphs is proposed. These complete graphs are joined to each other and to the remaining nonmodified graphs by means of new edges and by using a special dia

Large Cayley graphs and vertex-transitiv
Large Cayley graphs and vertex-transitive non-Cayley graphs of given degree and diameter
✍ Heather Macbeth; Jana Ε iagiovΓ‘; Jozef Ε irÑň; TomΓ‘Ε‘ VetrΓ­k πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 128 KB

## Abstract For any __d__β©Ύ5 and __k__β©Ύ3 we construct a family of Cayley graphs of degree __d__, diameter __k__, and order at least __k__((__d__βˆ’3)/3)^__k__^. By comparison with other available results in this area we show that our family gives the largest currently known Cayley graphs for a wide ra

A Note on Large Graphs of Diameter Two a
A Note on Large Graphs of Diameter Two and Given Maximum Degree
✍ Brendan D McKay; Mirka Miller; Jozef Ε irÑň πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 242 KB

Let vt(d, 2) be the largest order of a vertex-transitive graph of degree d and diameter 2. It is known that vt(d, 2)=d 2 +1 for d=1, 2, 3, and 7; for the remaining values of d we have vt(d, 2) d 2 &1. The only known general lower bound on vt(d, 2), valid for all d, seems to be vt(d, 2) w(d+2)Γ‚2x W(d

Constructions of large planar networks w
Constructions of large planar networks with given degree and diameter
✍ Fellows, M.; Hell, P.; Seyffarth, K. πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 157 KB πŸ‘ 3 views

There is considerable interest in constructing large networks with given diameter and maximum degree. In certain applications, there is a natural restriction for the networks to be planar. Thus, consider the problem of determining the maximum number of nodes in a planar network with maximum degree D