Multiplicative Versions of First Zagreb Index
نویسندگان
چکیده
The first Zagreb index of a graph G, with vertex set V (G) and edge set E(G), is defined as M1(G) = ∑ u∈V (G) d(u) 2 where d(u) denotes the degree of the vertex v. An alternative expression for M1(G) is ∑ uv∈E(G)[d(u) + d(v)]. We consider a multiplicative version of M1 defined as Π∗1(G) = ∏ uv∈E(G)[d(u) + d(v)]. We prove that among all connected graphs with a given number of vertices, the path has minimal Π∗1. We also determine the trees with the second–minimal Π∗1.
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