The Endomorphism Monoids Of Circulant Complete Graphs K(7m,7)

Graphs and their endomorphism monoid, which are the connection between the graph theory and semigroup algebraic theory, are the main research subject of algebraic graph theory. In this dissertation, The main research contents are to study the algebraic structures and properties of endomorphism monoid of circulant complete graph K(7m,7) with the combination structures of graphs.There are two chapters in this paper. The first chapter gives the study background.The second chapter mainly studies the endomorphism monoid structure of K(7m,7) The endomorphism monoids of the graph K(7m,7) are regular will be certified, and the endomorphism monoids of K(7m,7) are not orthodox semigroup, the automorphism group of K(7m,7) will be depicted. Its endomorphism type and endomorphism spec-trum will be obtained, and its enumeration problems of endomorphism monoids will be resolved.