5 research outputs found

    On strongly closed subgraphs of highly regular graphs

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    AbstractA geodetically closed induced subgraph Δ of a graph Γ is defined to be strongly closed if Γi(α) ∩ Γ1(β) stays in Δ for every i and α, β ϵ Δ with ∂(α, β) = i. We study the existence conditions of strongly closed subgraphs in highly regular graphs such as distance-regular graphs or distance-biregular graphs

    Distance-regular graphs

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    This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page

    Distance-Biregular Graphs and Orthogonal Polynomials

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    This thesis is about distance-biregular graphs– when they exist, what algebraic and structural properties they have, and how they arise in extremal problems. We develop a set of necessary conditions for a distance-biregular graph to exist. Using these conditions and a computer, we develop tables of possible parameter sets for distancebiregular graphs. We extend results of Fiol, Garriga, and Yebra characterizing distance-regular graphs to characterizations of distance-biregular graphs, and highlight some new results using these characterizations. We also extend the spectral Moore bounds of Cioaba et al. to semiregular bipartite graphs, and show that distance-biregular graphs arise as extremal examples of graphs meeting the spectral Moore bound

    On uniformly geodetic graphs

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    In this paper we study uniformly geodetic graphs. We shall give a diameter bound for these graphs. Further we characterize bipartite uniformly geodetic graphs and give some examples of them. In the last section we give two constructions and give sufficient conditions to assure that we get uniformly geodetic graphs from these constructions
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