The Endomorphism Monoids Of A Certain Class Of Circulant Complete Graphs

Graphs and their endomorphism monoids, which belong to interdisciplinary of graph theory and semigroup algebraic theory, are the important research direction of algebraic graph theory. The main research contents are to study the combination structures of graphs, the algebraic structures and properties of endomorphism monoids, and to consider the connection between them. The researches on endomorphism of graphs and their endomorphisni monoids will not only enrich the research contents of graph theory and the theory of semigroups, but also play an active role in promoting the intersection and merging of algebra with other discipline areas.In this dissertation, the endomorphism of circulant complete graph K(6m,6) and their endomorphism monoids will be studied. The endomorphisms monoid of the graph K(6m,6) is regular will be proved, the automorphism group of K(6m,G) will be determined, its endo-morphism spectrum and endomorphism type will be shown, and its enumeration problems of endomorphism monoids will be solved.