On mixed Moore graphs
نویسندگان
چکیده
منابع مشابه
A revised Moore bound for mixed graphs
The degree-diameter problem seeks to find the maximum possible order of a graph with a given (maximum) degree and diameter. It is known that graphs attaining the maximum possible value (the Moore bound) are extremely rare, but much activity is focussed on finding new examples of graphs or families of graph with orders approaching the bound as closely as possible. There has been recent interest ...
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Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their existence has been considered before for directed graphs and undirected ones, but not for the mixed case, which is a kind of generalization. In this paper we give some necessary c...
متن کاملNew mixed Moore graphs and directed strongly regular graphs
A 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 ...
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We give an upper bound for the number of vertices in mixed abelian Cayley graphs with given degree and diameter.
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We prove here a well known result in graph theory, originally proved by Hoffman and Singleton, that any non-trivial Moore graph of diameter 2 is regular of degree k = 2, 3, 7 or 57. The existence (and uniqueness) of these graphs is known for k = 2, 3, 7 while it is still an open problem if there is a moore graph of degree 57 or not.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.11.046