Explain the relationship between electoral college and executive branch

Article II of the Constitution establishes the Executive branch of the federal government. It defines the office of President and Vice President, and an Electoral College to elect them ... The executive Power shall be vested in a President of the United States of America.

The Electoral College is the system devised by the United States Constitution framers to provide a consistent method of election of the highest representative of the Executive Branch: the President of the United States, as well as the Vicepresident.