NDLI: Completely regular clique graphs

Content Provider	Springer Nature Link
Author	Suzuki, Hiroshi
Copyright Year	2013
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.
Starting Page	233
Ending Page	244
Page Count	12
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	40
Issue Number	1
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2013-11-05
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Distance-regular graph Association scheme Subconstituent algebra Terwilliger algebra Completely regular code Distance-semiregular graph Combinatorics Convex and Discrete Geometry Order, Lattices, Ordered Algebraic Structures Computer Science Group Theory and Generalizations
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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Completely regular clique graphs