Zagreb Indices and Multiplicative Zagreb Indices of Eulerian Graphs.

For a graph G=(V(G),E(G)), let d(u), d(v) be the degrees of the vertices u, v in G. The first and second Zagreb indices of G are defined as M1(G)=∑u∈V(G)d(u)2 and M2(G)=∑uv∈E(G)d(u)d(v), respectively. The first (generalized) and second Multiplicative Zagreb indices of G are defined as Π1,c(G)=∏v∈V(G)d(v)c and Π2(G)=Πuv∈E(G)d(u)d(v), respectively. The (Multiplicative) Zagreb indices have been the focus of considerable research in computational chemistry dating back to Narumi and Katayama in 1980s. Denote by Gn the set of all Eulerian graphs of order n. In this paper, we characterize Eulerian graphs with first three smallest and largest Zagreb indices and Multiplicative Zagreb indices in Gn. [ABSTRACT FROM AUTHOR]