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Or, if you want them connected, let $G$ be a 6-cycle with an extra edge between vertices 1 and 3, and $H$ a 6-cycle with an extra edge between vertices 1 and 4.
Let $G$ be a 6-cycle and let $H$ be two 3-cycles.
Let $G$ be a 6-cycle and let $H$ be two 3-cycles.
Or, if you want them connected, let $G$ be a 6-cycle with an extra edge between vertices 1 and 3, and $H$ a 6-cycle with an extra edge between vertices 1 and 4.
