Distance-regular graphs with girth 3 or 4: I |
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Authors: | Paul Terwilliger |
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Institution: | Department of Mathematics, Ohio State University, Columbus, Ohio 43210 USA |
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Abstract: | We study the structure of a distance-regular graph Γ with girth 3 or 4. First, we find some relationships among the intersection numbers of Γ when Γ contains a cycle {u1, u2, u3, u4} with ?(u1, u3) = ?(u2, u4) = 2. These relationships imply the diameter d, valency k, and intersection numbers a1 and cd of Γ are related by . Next, we show subgraphs induced by vertex neighbourhoods in distance-regular graphs where cycles mentioned above do not exist are related to certain strongly regular graphs. |
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