1986
DOI: 10.1002/jgt.3190100211
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Some large graphs with given degree and diameter

Abstract: 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, diameter 3 and order 66 are presented, which improve the previously known orders for these values of A and D. By its construction, these graphs have a large automorphism group.

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Cited by 21 publications
(41 citation statements)
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“…Let f be a rectagraph with valency k. Then f has at most 2k vertices, with equality if and only if f is the k-cube. Therefore, k;+l(y)(i + I) ...,; N; ...,; k;(y)(ki); by induction we find k;(y) ...,; (7). Fix y E f, and let N; be the number of edges a/3 with a E f;(y) and /3 Ef;+l(Y)· By Proposition 1.…”
Section: 2 a Rectagraph Is Regular;mentioning
confidence: 88%
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“…Let f be a rectagraph with valency k. Then f has at most 2k vertices, with equality if and only if f is the k-cube. Therefore, k;+l(y)(i + I) ...,; N; ...,; k;(y)(ki); by induction we find k;(y) ...,; (7). Fix y E f, and let N; be the number of edges a/3 with a E f;(y) and /3 Ef;+l(Y)· By Proposition 1.…”
Section: 2 a Rectagraph Is Regular;mentioning
confidence: 88%
“…These families of examples overlap for small parameters: (v, a, I) = (7,2,3) is found under both b) and e), (v,a,/) = (13,3,3) under both d) and e) and (v,a,/) = (21,4,3) under both c) and e). These families of examples overlap for small parameters: (v, a, I) = (7,2,3) is found under both b) and e), (v,a,/) = (13,3,3) under both d) and e) and (v,a,/) = (21,4,3) under both c) and e).…”
Section: Problem Prove That No Other Examples Existmentioning
confidence: 93%
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