On mixed Moore graphs

Nguyen, Minh; Miller, Mirka; Gimbert, Joan

doi:10.1016/j.disc.2005.11.046

Cited by 34 publications

(36 citation statements)

References 6 publications

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“…Such a graph is called a mixed Moore graph. Nguyen, Miller and Gimbert [15] showed that every mixed Moore graph has diameter 2, and thus it is a directed strongly regular graph with λ = 0, µ = 1, k = t + z and n = k 2 + k − t + 1.…”

Section: Introductionmentioning

confidence: 99%

New mixed Moore graphs and directed strongly regular graphs

Jørgensen

2015

Discrete Mathematics

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a b s t r a c tA directed strongly regular graph with parameters (n, k, t, λ, µ) is a k-regular directed graph with n vertices satisfying that the number of walks of length 2 from a vertex x to a vertex y is t if x = y, λ if there is an edge directed from x to y and µ otherwise. If λ = 0 and µ = 1 then we say that it is a mixed Moore graph. It is known that there are unique mixed Moore graphs with parameters (k 2 + k, k, 1, 0, 1), k ≥ 2, and (18, 4, 3, 0, 1). We construct a new mixed Moore graph with parameters (108, 10, 3, 0, 1) and also new directed strongly regular graphs with parameters (36, 10, 5, 2, 3) and (96, 13, 5, 0, 2). This new graph on 108 vertices can also be seen as an example of a so called multipartite Moore digraph. Finally we consider the possibility that mixed Moore graphs with other parameters could exist, in particular the first open case which is (40, 6, 3, 0, 1).

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Section: Introductionmentioning

confidence: 99%

New mixed Moore graphs and directed strongly regular graphs

Jørgensen

2015

Discrete Mathematics

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“…For more specific results concerning mixed graphs, which are the topic of this article, see, for example, Nguyen and Miller , and Nguyen et al. .…”

Section: Introductionmentioning

confidence: 99%

“…In general, Nguyen et al. showed that mixed graphs with

r, z \geq 0

(or mixed Moore graphs ) only exist for diameter

k = 2

.…”

Section: Introductionmentioning

confidence: 99%

On bipartite‐mixed graphs

Dalfó¹,

Fiol

López

2018

Journal of Graph Theory

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“…Note that proper mixed Moore graphs do not exist for k ≥ 3 (see [9]). For k = 2, the known proper mixed Moore graphs are the Kautz digraphs and the Bosák graph (see Fig.…”

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confidence: 98%

“…2). However, the problem concerning the existence of many proper mixed Moore graphs of k = 2 still remains open (see [3,9]). Since mixed Moore graphs of diameter k ≥ 3 do not exist, it is natural to ask the following question.…”

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confidence: 99%