All Maximal Clones of a Majority Reflexive Graph

Udom Chotwattakawanit, Chawewan Rattanaprasert

Abstract


Reflexive graphs are extensively investigated not only in graph

theory but also in the context of universal algebra. For examples,

Bandelt \cite{B} characterized all majority reflexive graphs;

i.e., reflexive graphs having an edge-preserving majority

operation; and Johansen \cite{J} constructed a duality for a

reflexive graph. In this paper, we characterize all maximal clones

containing the clone of all operations preserving edges of a

majority reflexive graph. Our results together with NU-duality

Theorem \cite{CD} imply a duality for a tolerance-primal algebra

having a majority term operation.


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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|