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In the present paper, we study the upper and lower bounds for the number offacets of symmetric edge polytopes of connected graphs conjectured by Braun andBruegge. In particular, we show that their conjecture is true for any graphthat is the join of two graphs (equivalently, for any connected graph whosecomplement graph is not connected). It is known that any symmetric edgepolytope is a centrally symmetric reflexive polytope. Hence our results give apartial answer to Nill's conjecture: the number of facets of a $d$-dimensionalreflexive polytope is at most $6^{d/2}$.

Number of facets of symmetric edge polytopes arising from join graphs