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
Large bipartite Cayley graphs of given degree and diameter
✍ Scribed by Tomáš Vetrík; Rinovia Simanjuntak; Edy Tri Baskoro
- Book ID
- 108114278
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 181 KB
- Volume
- 311
- Category
- Article
- ISSN
- 0012-365X
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## Abstract For any __d__⩾5 and __k__⩾3 we construct a family of Cayley graphs of degree __d__, diameter __k__, and order at least __k__((__d__−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
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