A graph G is called End-regular, if every endomorphism of G is regular as a monoid. In this article, we investigate End-regularity of bicycle graphs. Moreover, a generalization of bicycle graph is defined and gives a characterization of End-regular generalized bicycle graphs. Furthermore, properties End-idempotent-closed and End-orthodox have been considered for these graphs. Finally, it has been proved that when join of two generalized bicycle graphs is End-regular.
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