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A note on constructing large Cayley graphs of given degree and diameter by voltage assignments
, 1998
"... Voltage graphs are a powerful tool for constructing large graphs (called lifts) with prescribed properties as covering spaces of small base graphs. This makes them suitable for application to the degree/diameter problem, which is to determine the largest order of a graph with given degree and diame ..."
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Cited by 6 (1 self)
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Voltage graphs are a powerful tool for constructing large graphs (called lifts) with prescribed properties as covering spaces of small base graphs. This makes them suitable for application to the degree/diameter problem, which is to determine the largest order of a graph with given degree
Large vertextransitive and Cayley graphs with given degree and diameter Abstract
"... We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d = 3m − 1 and diameter k ≥ 3 of order km k. By comparison with other avai ..."
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We present an upper bound on the number of vertices in graphs of given degree and diameter 3 that arise as lifts of dipoles with voltage assignments in Abelian groups. Further, we construct a family of Cayley graphs of degree d = 3m − 1 and diameter k ≥ 3 of order km k. By comparison with other
A Note on Large Graphs of Diameter Two and Given Maximum Degree
"... Let vt(d; 2) be the largest order of a vertextransitive graph of degree d and diameter two. 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 \Gamma 1. The only known general lower bound on vt(d; 2), valid for all d, seems to be vt(d ..."
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Cited by 28 (6 self)
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(d; 2) b d+2 2 cd d+2 2 e. Using voltage graphs, we construct a family of vertextransitive nonCayley graphs which shows that vt(d; 2) 8 9 (d + 1 2 ) 2 for all d of the form d = (3q \Gamma 1)=2 where q is a prime power congruent with 1 (mod 4). The construction generalizes to all prime
A NOTE ON A GEOMETRIC CONSTRUCTION OF LARGE CAYLEY GRAPHS OF GIVEN DEGREE AND DIAMETER
"... Abstract. An infinite series and some sporadic examples of large Cayley graphs with given degree and diameter are constructed. The graphs arise from arcs, caps and other objects of finite projective spaces. A simple finite graph Γ is a (∆, D)graph if it has maximum degree ∆, and diameter at most D. ..."
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Abstract. An infinite series and some sporadic examples of large Cayley graphs with given degree and diameter are constructed. The graphs arise from arcs, caps and other objects of finite projective spaces. A simple finite graph Γ is a (∆, D)graph if it has maximum degree ∆, and diameter at most D
Degree/Diameter , , Cayley G
, 2004
"... iv The Degree/Diameter problem has been studied for a long time and still have’t been solved completely.We take a whole analysis on it and give two main solutions to it in this paper.One is through constructing a Cayley graph on the semiproduct of two cyclic groups,another is by lifting a small bas ..."
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iv The Degree/Diameter problem has been studied for a long time and still have’t been solved completely.We take a whole analysis on it and give two main solutions to it in this paper.One is through constructing a Cayley graph on the semiproduct of two cyclic groups,another is by lifting a small
Large digraphs with small diameter: A voltage assignment approach
"... The theory of lifting voltage digraphs provides a useful tool for constructing large digraphs with given properties from suitable small base digraphs endowed with an assignment of voltages (=elements of a finite group) on arcs. We revisit the degree/diameter problem for digraphs from this new perspe ..."
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Cited by 4 (2 self)
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The theory of lifting voltage digraphs provides a useful tool for constructing large digraphs with given properties from suitable small base digraphs endowed with an assignment of voltages (=elements of a finite group) on arcs. We revisit the degree/diameter problem for digraphs from this new
Moore graphs and beyond: A survey of the degree/diameter problem
 ELECTRONIC JOURNAL OF COMBINATORICS
, 2013
"... The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. General upper bounds – called Moore bounds – for the order of such graphs and digraphs are attainable only for certain special graphs and digraphs. Finding better (tighter) upper bo ..."
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Cited by 67 (7 self)
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bounds for the maximum possible number of vertices, given the other two parameters, and thus attacking the degree/diameter problem ‘from above’, remains a largely unexplored area. Constructions producing large graphs and digraphs of given degree and diameter represent a way of attacking the degree/diameter
MacroStar Networks: Efficient LowDegree Alternatives to Star Graphs for LargeScale Parallel Architectures
 IEEE Trans. Parallel Distrib. Sys
, 1996
"... We propose a new class of interconnection networks called macrostar networks, which belong to the class of Cayley graphs and use the star graph as a basic building module. A macrostar network can have node degree that is considerably smaller than that of a star graph of the same size, and diameter ..."
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Cited by 13 (5 self)
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, and diameter that is asymptotically within a factor of 1.25 from a universal lower bound (given its node degree) . We show that algorithms developed for star graphs can be emulated on suitably constructed macrostars with asymptotically optimal slowdown. In particular, we obtain asymptotically optimal
A BoundedDegree Network Formation Game
 In PODC ’08
"... Motivated by applications in peertopeer and overlay networks we define and study the Bounded Degree Network Formation (BDNF) game. In an (n, k)BDNF game, we are given n nodes, a bound k on the outdegree of each node, and a weight wvu for each ordered pair (v, u) representing the traffic rate fro ..."
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Cited by 7 (6 self)
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special family of regular wirings, the class of Abelian Cayley graphs, in which all nodes imitate the same wiring pattern, and show that if n is sufficiently large no such regular wiring can be a pure Nash equilibrium. 1
3esis Supervisor Accepted by
, 2005
"... in partial ful2llment of the requirements for the degree of ..."
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