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In this research paper, https://mp.feri.um.si/osebne/peterin/clanki/edimproduct5.pdf
Theorem 1: For any non trivial graphs G and H,
edim(G ∨ H) = { |V (G)| + |V (H)| − 1, if G ∈ G or H ∈ G,
|V (G)| + |V (H)| − 2, if G, H /∈ G.
As a corollary based on this theorem, a complete bipartite graph G2,2 has edim (G) = 2, and any multipartite graph G(,ri,r2,...rn) with k larger than 2 will have edim(G) = ∑(ri-1) with i = [1,n]. This implies that the tripartite G(1,1,3) will have edim(G)=2, and this tripartite graph is also a fan graph (3,2). The rules for fan graphs in resource 3 are only for fan graphs (1,n), so I am not sure of my undertaking.
P.S. Because I can't write mathematical notations here, I would prefer you read it from the original research paper. The theorem is in page 3 and the corollary is in page 4
Theorem 1: For any non trivial graphs G and H,
edim(G ∨ H) = { |V (G)| + |V (H)| − 1, if G ∈ G or H ∈ G,
|V (G)| + |V (H)| − 2, if G, H /∈ G.
As a corollary based on this theorem, a complete bipartite graph G2,2 has edim (G) = 2, and any multipartite graph G(,ri,r2,...rn) with k larger than 2 will have edim(G) = ∑(ri-1) with i = [1,n]. This implies that the tripartite G(1,1,3) will have edim(G)=2, and this tripartite graph is also a fan graph (3,2). The rules for fan graphs in resource 3 are only for fan graphs (1,n), so I am not sure of my undertaking.
P.S. Because I can't write mathematical notations here, I would prefer you read it from the original research paper. The theorem is in page 3 and the corollary is in page 4