Cages—a survey

Wong, Pak-Ken

doi:10.1002/jgt.3190060103

Cited by 167 publications

(96 citation statements)

References 49 publications

(36 reference statements)

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“…Based survey on cages ( [17]), the following results can be stated. The goalminimality was verified by a computer, except of the first three cases.…”

Section: Goal-minimal Properties Of Cages a K-regular Graph (K ≥ 2) Wmentioning

confidence: 99%

“…We know from [17] that the unique (k, 2n)-cage is the incidence graph of a generalized n-gon of order q. Hence we have:…”

Section: ä ññ 1º ([5]) An Incidence Structure γ = (P L I) Is a Genmentioning

confidence: 99%

“…Three of his graphs are 3-GMD. For a survey of cage graphs we refer the reader to the website of R o y l e [15] or to the paper [17].…”

Section: ä ññ 1º ([5]) An Incidence Structure γ = (P L I) Is a Genmentioning

confidence: 99%

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Goal-minimally k-elongated graphs

Gyürki

2009

Mathematica Slovaca

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ABSTRACT. Let k be an integer. A 2-edge connected graph G is said to be goal-minimally k-elongated (k-GME) if for every edge uv ∈ E(G) the inequality d G−uv (x, y) > k holds if and only if {u, v} = {x, y}. In particular, if the integer k is equal to the diameter of graph G, we get the goal-minimally k-diametric (k-GMD) graphs. In this paper we construct some infinite families of GME graphs and explore k-GME and k-GMD properties of cages.

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“…Based survey on cages ( [17]), the following results can be stated. The goalminimality was verified by a computer, except of the first three cases.…”

Section: Goal-minimal Properties Of Cages a K-regular Graph (K ≥ 2) Wmentioning

confidence: 99%

“…We know from [17] that the unique (k, 2n)-cage is the incidence graph of a generalized n-gon of order q. Hence we have:…”

Section: ä ññ 1º ([5]) An Incidence Structure γ = (P L I) Is a Genmentioning

confidence: 99%

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Goal-minimally k-elongated graphs

Gyürki

2009

Mathematica Slovaca

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“…See the Appendix and Ref. [7]. By deleting two directly connected ternary links in this cage, we regain the three (I,7)-primegraphs again, as there are three non-isomorphic ways to carry this out.…”

Section: Look-out For Pnme-chains With a Prescribed Number Of Mobilitmentioning

confidence: 99%

Look-out for prime-chains with a prescribed number of mobility-degrees of freedom

Dijksman

Timmermans

1994

Mechanism and Machine Theory

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“…It is hoped That this raph may be useful in The search of a (3,9)-cage. (3,9) be the number of vertices of a (3,9)-cage. It is known that 54 < f(3,9) < 58 (see [I] (see [2] and [3]).…”

mentioning

confidence: 99%