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Graph TheoryEasyEulerian and Hamiltonian Graphs

Eulerian and Hamiltonian Graphs · Easy problem

A "barbell" graph has two squares, 1-2-3-4-11\text{-}2\text{-}3\text{-}4\text{-}1 and 5-6-7-8-55\text{-}6\text{-}7\text{-}8\text{-}5, joined by TWO separate bridge edges both between 11 and 55 (so 1515 is a doubled edge, 1010 edges total). How many vertices of this multigraph have odd degree?