Completely regular clique graphs |
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Authors: | Hiroshi Suzuki |
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Institution: | 1. International Christian University, Mitaka, Tokyo, 181-8585, Japan
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Abstract: | Let Γ=(X,R) be a connected graph. Then Γ is said to be a completely regular clique graph of parameters (s,c) with s≥1 and c≥1, if there is a collection \(\mathcal{C}\) of completely regular cliques of size s+1 such that every edge is contained in exactly c members of \(\mathcal{C}\) . In this paper, we show that the parameters of \(C\in\mathcal{C}\) as a completely regular code do not depend on \(C\in\mathcal{C}\) . As a by-product we have that all completely regular clique graphs are distance-regular whenever \(\mathcal {C}\) consists of edges. We investigate the case when Γ is distance-regular, and show that Γ is a completely regular clique graph if and only if it is a bipartite half of a distance-semiregular graph. |
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